Answers
Answer:
The second photo.
Step-by-step explanation:
If you use a graphing calculator, you can easily find the answer.
Answer:
see below
Step-by-step explanation:
Comparing the given equation to the standard-form equation of a circle ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r
we find that ...
h = 2, k = -5, r = 2
So, the circle you're looking for is centered at (2, -5) and has a radius of 2.
Related Questions
find the standard deviation of the data set 8.2,10.1,2.6,4.8,2.4,5.6,7.0,3.3. Round to the nearest hundredth if necessary.
Answers
Final answer:
The standard deviation of the data set is 2.98, calculated by finding the mean, squaring the differences, averaging them, and taking the square root. One standard deviation below the mean is 2.52.
Explanation:
To find the standard deviation of the data set 8.2, 10.1, 2.6, 4.8, 2.4, 5.6, 7.0, 3.3, follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data point and square the result.
Calculate the average of these squared differences.
Take the square root of the average to find the standard deviation.
Using a calculator or computer:
The mean of the data set is 5.5
The squared differences would be (8.2-5.5)^2, (10.1-5.5)^2, etc.
The average of these squared differences is approximately 8.86.
The square root of 8.86 gives us the standard deviation of approximately 2.98.
Therefore, the standard deviation of the data set, rounded to the nearest hundredth, is 2.98.
To find the value that is one standard deviation below the mean, you subtract the standard deviation from the mean:
5.5 - 2.98 = 2.52.
If $.30 out of every one dollar goes to taxes and the rest is net income what is the ratio of taxes to net income
Answers
3:7
Taxes are 30c and one dollar is 100c then the net income is 70c, making the income 30:70. this can be simplified to 3:7.
(98 POINTS) (PLEASE HURRY!)
[1] x^2 - xy - x + y =
[2] 1 - x - x^2 + x^3 =
[3] xy + 1 + x + y =
[4] x^2y + y^2x + x^2x + y^3 =
Answers
Answer:
1. no like terms
2. x^ 3 − x^ 2 − x + 1
3.x y + x + y + 1
4.x^ 3 + x^ 2 y + x y^ 2 + y^ 3
Lol
You play a board game with your little brother. You pick a card that sends you back five spaces. On your next turn, you must move back three more spaces. On your third turn, you get to move forward three spaces. Which expression best shows how you could find your new spot on the game board?
Answers
Answer:
Step-by-step explanation:
- 5 + (-3) + 3 is the correct option.
Answer:
-5 + (-3) + 3
Step-by-step explanation:
A number by which another number is to be divided
Answers
Answer:
Dividend
Step-by-step explanation:
If you take a simple division problem like A = B / C
A is the quotient (result)
B is the dividend
C is the divisor
So, a number by which another number is to be divided is called a dividend, like A in the example above.
If C doesn't divide B in an exact manner (like in the case of 7 / 2), there's a remainder for the operation.
A divisor is a number by which another number, the dividend, is divided. In scientific notation, division involves dividing the coefficients and subtracting the exponents of the divisor from the dividend. Division is fundamentally related to multiplication, as it can be represented by multiplying by a reciprocal.
A fair coin is tossed 3 times. What is the probability that the coin with land showing heads on all three tosses.
Answers
Answer:2/3
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
one way we can solve this is by making a tree using H for heads and T for tails
since it can land H or T, we put them down like this. then we can get H or T again because its a coin, so we put that under each letter. finally we do the same thing again to get 8 possibilities. now we can count how many of them was HHH, which is one
H T
/ \ / \
H T H T
/\ /\ /\ /\
H T H T H T H T
^ this one
or do 2 x 2 x 2 because there are 2 possibilities each three times
You invest $3000 in an account at 3.5% per year simple interest. How much will you have in the account at the beginning of the 7th year? Round your answer to the nearest whole dollar.
Answers
Answer:
$3735
Step-by-step explanation:
The formula for simple interest is I = Prt, where I is the interest earned, P is the initial investment, r is the interest rate in decimal form, and t is the time in years. We have everything we need to find the interest, which is the amount your investment earned while it sat there for 7 years. Once we find that interest amount, we will add it to the intial investment to find the total amount after 7 years that your money has grown to.
I = 3000(.035)(7) so
I = 735
3000 + 735 = 3735
Answer:
$3,630
Step-by-step explanation:
You invest $3,000 in an account at 3.5% per year simple interest.
We have to calculate the amount in the account at the beginning of the 7th year. This means we have to calculate the interest for completed 6 years.
Formula for simple interest
A = P(1+rt)
A = Amount after maturity
P = Principal amount ( 3,000)
r = rate of interest in decimal ( 0.035)
t = time in years ( 6 )
Now we put the values in to formula
A = 3,000(1 + 0.035 × 6)
A = 3,000 ( 1 + 0.021 )
A = 3,000 × 1.21
A = $3,630
The amount would be $3,630 at the beginning of the 7th year.
NEED HELP ASAP PRETTY PLEASE WITH A CHERRY ON TOP WILL GIVE A FOOT RUB IF REQUESTED ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Solve the equation check for extraneous solutions 4|5-5x|=7x+6
Answers
Answer:
[tex]\large\boxed{b.\ x=\dfrac{14}{27}\ \text{and}\ c.\ x=2}[/tex]
Step-by-step explanation:
[tex]4|5-5x|=7x+6\\4|-5(x-1)|=7x+6\\4|-5||x-1|=7x+6\\(4)(5)|x-1|=7x+6\\20|x-1|=7x+6\\\\\text{First step:}\\\text{Based on the de}\text{finition of the absolute value}\\\\|x-1|=\left\{\begin{array}{ccc}x-1&\text{for}\ x\geq1\\1-x&\text{for}\ x<1\end{array}\right\\\\\text{Let}\ x<1\to x\in(-\infty,\ 1).\ \text{Then}\ |x-1|=1-x:\\\\20(1-x)=7x+6\qquad\text{use the distributive property}\\20-20x=7x+6\qquad\text{subtract 20 from both sides}\\-20x=7x-14\qquad\text{subtract}\ 7x\ \text{from both sides}\\-27x=-14\qquad\text{divide both sides by (-27)}\\x=\dfrac{14}{27}<1\qquad \bold{:)}[/tex]
[tex]\text{Let}\ x\geq0\to x\in\left<1,\ \infty\right).\ \text{Then}\ |x-1|=x-1:\\\\20(x-1)=7x+6\qquad\text{use the distributive property}\\20x-20=7x+6\qquad\text{add 20 to both sides}\\20x=7x+26\qquad\text{subtract}\ 7x\ \text{from both sides}\\13x=26\qquad\text{divide both sides by 13}\\x=2\geq1\qquad \bold{:)}[/tex]
circle O is shown below. the diagram is not drawn to scale. 73°
Answers
53.5
Explanation:
Since triangle AOB is an isosceles triangle (AO = OB), the base angles of the triangle are 53.5. (180-73 = 107, 107/2 = 53.5)
Answer:
Option A
53.5
Step-by-step explanation:
Cartesian coordinates are given below for two points.
a. 3,1
b.5, 11 for each point: find the polar coordinates r, , where r 0 and 0 2 . find the polar coordinates r, , where r 0 and 0 2 . give exact answers for all points.
Answers
I don’t know what the answer is I wish I could help
Find the volume of the rectangular prism. Write answer as a fraction. Length=2/3 mm. Width=1/3mm. Height=2/3 mm.
Answers
put simply, the volume of a rectangular prism is just the product of all its 3 dimensions.
[tex]\bf V=\cfrac{2}{3}\cdot \cfrac{1}{3}\cdot \cfrac{2}{3}\implies V=\cfrac{4}{27}[/tex]
Identify the coefficient of 13m
Answers
Answer: the coefficient of 13m is 13.
Answer:
The coefficient of 13 m is 13.
Step-by-step explanation:
Consider the provided expression.
[tex]13m[/tex]
Numbers appear with variables are called coefficients.
Alphabets in an expression are called variables.
Numbers appear without variables are called Constant terms.
Here we need to identity the coefficient.
From the above definition we know the number appear with the variables are coefficients.
Since m is variable, thus the number 13 must be the coefficient.
Hence, the coefficient of 13 m is 13.
Which trigonometric function requires a domain restriction of [-pi/2, pi/2] to make it invertable?
Answers
Answer:
[tex]y=\tan x[/tex]
Step-by-step explanation:
The trigonometric function that needs a domain restriction of [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex] to make it invertible is [tex]y=\tan x[/tex].
The function [tex]y=\tan x[/tex] will pass the horizontal line test on this interval therefore making it an invertible function on this interval.
This explains why the inverse tangent function, [tex]y=\tan^{-1} x[/tex] has range [tex][-\frac{\pi}{2},\frac{\pi}{2} ][/tex].
Answer:
A) [tex]f(x)=sin x[/tex]
Step-by-step explanation:
I just did the test and this was the correct answer.
Find the length of each leg. Leave answer in simplest radical form.
Question 28 options:
16√2
8
8√2
4√2
Answers
Answer:
8√2
Step-by-step explanation:
The hypotenuse of a right triangle is √2 times the leg length, so you have ...
[tex]x\sqrt{2}=16[/tex]
Dividing by the coefficient of x gives ...
[tex]x=\dfrac{16}{\sqrt{2}}=\dfrac{16\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=8\sqrt{2}[/tex]
Each leg has length 8√2.
You are installing a brick sidewalk. The brick portion of the sidewalk will occupy an area of 100 feet long by 4 feet wide. Each brick will occupy an area 8 inches long by 4 inches wide. What is the minimum number of bricks you will need to build the sidewalk?
Answers
Answer:
1,800 bricks are needed
Step-by-step explanation:
First convert the Length and width of the sidewalk into inches
Entire Sidewalk: L= 100x12 =1200in and W= 4 x 12 = 48in
Then we know Area = LxW, so we will do this for both the sidewalk and the brick.
Area of sidewalk: 1200 x 48 = 57600
Bricks ( no need to convert since the measurements are already in inches): 8 x 4 = 32
Now we will divide the area of the entire sidewalk by the area of a single brick to find out how many bricks you need to complete the whole sidewalk:
57600/32= 1,800 bricks
The following binomials are multiplied together as shown below. Which of the following is a true statement?
(x+y)(a+b)
= xa+xb+ya+yb
A. There is no error; the binomials were correctly multiplied together.
B. Binomials with different variables cannot be multiplied together.
C. The product was not simplified correctly.
D. There should only be three terms when multiplying two binomials.
Answers
For this case we have that by definition:
[tex](a + b) (c + d)[/tex] is equal to:
[tex]ac + ad + bc + bd[/tex]
Applying the distributive property.
Then, it can be seen that the given binomials were multiplied correctly.
ANswer:
There is no error; the binomials were correctly multiplied together.
Triangle TUV has been dilated to form triangle TꞌUꞌVꞌ.
What is the scale factor?
Answers
Answer:
4.4, 4.4 : 1, 22 : 5
Step-by-step explanation:
There are many ways to solve this, but I'll do it by finding the ratio between V'T' and VT.
That's easy, we're given the lengths of these two. The ratio would be 8.8/2. 8.8/2 = 4.4, or (8.8*5)/(2*5) = 22/5
In a simple random sample of 90 patients who saw a certain dentist, 8 patients had their teeth whitened. Which interval is the 95% confidence interval for the percent of all the dentists patients who had their teeth whitened?
Answers
Answer:
(3.01%, 14.77%)
Step-by-step explanation:
The confidence interval of a proportion is:
CI = p ± SE × CV,
where p is the proportion, SE is the standard error, and CV is the critical value (either a t-score or a z-score).
We already know the proportion: 8/90. But we need to find the standard error and the critical value.
The standard error is:
SE = √(p (1-p) / n)
SE = √((8/90) * (82/90) / 90)
SE = 0.03
To find the critical value, we must first find the alpha level and the degrees of freedom.
The alpha level for a 95% confidence interval is:
α = (1 - 0.95) / 2 = 0.025
The degrees of freedom is one less than the sample size:
df = n - 1 = 90 - 1 = 89
Since df > 30, we can approximate this with a normal distribution.
If we look up the alpha level in a z score table, we find the z-score is 1.96. That's our critical value. CV = 1.96.
Now we can find the confidence interval:
CI = 8/90 ± 0.03 * 1.96
CI = 0.0889 ± 0.0588
CI = (0.0301, 0.1477)
So we are 95% confident that the percent of patients who had their teeth whitened is between 3.01% and 14.77%.
Given that g(x)=3x^2 -4x+3, find each of the following.
PICTURE DOWN BELOW!!!
Answers
Answer:
see explanation
Step-by-step explanation:
To evaluate the expression for the given values.
Substitute the given values for x into g(x)
a
g(0) = 3(0)² - 4(0) + 3 = 0 - 0 + 3 = 3
b
g(- 1) = 3(- 1)² - 4(- 1) + 3 = 3 + 4 + 3 = 10
c
g(2) = 3(2)² - 4(2) + 3 = 12 - 8 + 3 = 7
d
g(- x) = 3(- x)² - 4(- x) + 3 = 3x² + 4x + 3
e
g(1 - t)
= 3(1 - t)² - 4(1 - t) + 3
= 3(1 - 2t + t²) - 4 + 4t + 3
= 3 - 6t + 3t² - 4 + 4t + 3
= 3t² - 2t + 2
A scatter plot containing the point (5, 29) has the regression equation yˆ=5x+2 . What is the residual e when x = 5? Enter your answer in the box.
e = ?
Answers
Answer:
The answer is below
Step-by-step explanation:
Answer:
The residual e=2 when x = 5.
Step-by-step explanation:
A scatter plot containing the point (5, 29), it means the observed value at x=5 it 29.
The given regression equation is
[tex]\hat{y}=5x+2[/tex]
Substitute x=5 in the above regression equation, to find the predicted value at x=-5.
[tex]\hat{y}=5(5)+2=25+2=27[/tex]
The formula to find the residual value e is
e = Observed value - Predicted value
[tex]e=29-27[/tex]
[tex]e=2[/tex]
Therefore the residual e=2 when x = 5.
mariela is standing in a building and looking out a window at a tree. The tree is 20 feet away from Mariela, Mariela's line of sight creates a 42 degree angle of elevation, and her line of sight creates a 31 degree of depression. What is the height, in feet, of the tree?
Answers
Answer: 30.01 feet.
Step-by-step explanation:
You need to remember this identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
Observe the figure attached, where [tex]h_t[/tex] is the height in feet of the tree.
You need to calculate [tex]h_1[/tex] of the Triangle 1, where:
[tex]\alpha= \alpha_1=42\°\\opposite=h_1\\adjacent=20[/tex]
Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_1[/tex]:
[tex]tan(42\°)=\frac{h_1}{20}\\\\h_1=20*tan(42\°)\\h_1=18[/tex]
Now you need to calculate [tex]h_2[/tex] of the Triangle 2, where:
[tex]\alpha= \alpha_2=31\°\\opposite=h_2\\adjacent=20[/tex]
Substitute values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for [tex]h_2[/tex]:
[tex]tan(31\°)=\frac{h_2}{20}\\\\h_2=20*tan(31\°)\\h_2=12.01[/tex]
Then the height in feet of the tree is:
[tex]h_t=h_1+h_2\\h_t=(18+12.01)ft\\h_t=30.01ft[/tex]
The height of the tree can be determined by the trigonometric ratio of tan angle.
The height of the tree is 30 feet.
Given that,
Mariela is standing in a building and looking out a window at a tree.
The tree is 20 feet away from Mariela,
Mariela's line of sight creates a 42-degree angle of elevation, and her line of sight creates a 31 degree of depression.
We have to determine,
What is the height, in feet, of the tree?
According to the question,
Let, the height of the tree be h
The tree is 20 feet away from Mariela,
First, we have to calculate the length of BD which is x,
Then,
The length of BD is given by,
[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{BD}{AD}\\\\Tan42 = \dfrac{x}{20}\\\\x = tan42 \times 20\\\\x = 0.9 \times 20\\\\x = 18[/tex]
The measurement of x is 18 feet.
Again we have to calculate the length of y,
Then,
The length of DC is given by,
[tex]\rm Tan\theta = \dfrac{Opposite \ side}{Adjacent \ side}\\\\Tan\theta = \dfrac{DC}{AD}\\\\Tan31 = \dfrac{Y}{20}\\\\y = tan31 \times 20\\\\x =0.6 \times 20\\\\y = 12[/tex]
The measurement of y is 12 feet.
Therefore,
The height of the tree is given by,
[tex]\rm h= x +y\\\\h = 18+12\\\\h = 30 \ feet[/tex]
Hence, The height of the tree is 30 feet.
To know more about Trigonometry click the link given below.
https://brainly.com/question/7622474
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!
Answers
Answer:
[tex]\text{D.}\quad d=\dfrac{206-8(10)}{7}[/tex]
Step-by-step explanation:
The total length of the space between rungs is the overall length less the width of 8 rungs, so is 206 -8(10). That space is divided into 7 equal parts, as shown by the equation in choice D.
_____
Choice A looks similar, but is not. In that equation, only the term 8(10) is divided by 7. You want the difference to be divided by 7, so must have a grouping symbol of some kind. Choice D uses the division bar to group the terms of the numerator. Parentheses would work, too, as in ...
d = (206 -8(10))÷7
but without them, the equation is incorrect.
The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.25 0.25, and the sample statistics include n equals = 1588 1588 subjects with 413 413 saying that they smoked a cigarette in the past week. find the value of the test statistic.
Answers
Answer:
The test statistic supports the claim
Step-by-step explanation:
413 out of 1588 people says that they smoked.
So, we can find that that is 413/1588 ≈ 0.26 = 26%.
This proves that the test statistic is supporting the claim, since the two are similar.
The question is in the picture PLEASE HELP ME!!! idk how to do this
Answers
Answer:
35
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
nCk = n!/(k!(n -k)!)
7C3 = 7!/(3!(7-3)!) = 7·6·5/(3·2·1) = 7·5 = 35
_____
It is convenient to use the largest of the factorials in the denominator to cancel as many factors as you can from the numerator, then cancel factors from the remaining numbers. Here after canceling 4! = 4·3·2·1 from the numerator, we are left with 7·6·5 divided by 3! = 3·2·1 = 6. Obviously, this will cancel the 6 in the numerator product, leaving only 7·5 = 35.
Some graphing and/or scientific calculators will have this function built in.
The function f(t) = 4 cos(pi over 3t) + 15 represents the tide in Bright Sea. It has a maximum of 19 feet when time (t) is 0 and a minimum of 11 feet. The sea repeats this cycle every 6 hours. After five hours, how high is the tide?
13.5 feet
16 feet
18.5 feet
17 feet
Answers
Answer:
17 ft
Step-by-step explanation:
I don't think you meant to put pi over 3t ... I think you meant to put pi just over 3
Just plug in 5 assuming t is time in hours.
Evaluate 4 *cos(pi/3 *5)+15
which is 17 ft
The height of tower after 5 hours is 17.68 feet.
What is cosine range?
The graph of the cosine function looks like this: The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .
The Cosine function : f(t) = 4 cos(π/3t) + 15
and, f(t) = 4 cos(2kπ + π/3t) + 15
where k= 0,1,2,3....
The range of cosine function is : Maximum= +1 and minimum= -1
At t=0,
For maximum, f(t)= 4 x1 +15
= 19 feet
For minimum, f(t) = 4 x(-1)+15
= 11 feet
After , 6 hours ,the tide function is: 6 n=5
n= 6/5
f(t) = 4 cos ( 2* [tex]\frac{5* \pi}{6}[/tex] + [tex]\frac{\pi}{3*5}[/tex] ) +15
= 4 cos (26 π/15) + 15
= 4 cos[tex]312^{0}[/tex] + 15
= [tex]4 cos 48^{0}+ 15[/tex]
= 4 x 0.6691 +15
= 17.68 feet.
Thus, the height of tower after 5 hours is 17.68 feet
Learn more about concept here:
https://brainly.com/question/3714457
#SPJ2
What does the relationship between the mean and median reveal about the shape of the data? The mean is less than the median, so the data is skewed left. The mean is more than the median, so the data is skewed right. The mean is equal to the median, so the data is symmetrical. The mean is equal to the median, so the data is linear.
Answers
Answer:
The mean is equal to the median, so the data is symmetrical
Step-by-step explanation:
Here is the data.
10 5 8 10 12 6
8 10 15 6 12 18
The given data: 10 5 8 10 12 6 8 10 15 6 12 18
For finding the Mean, we will have to add all numbers together and divide it by total number. i.e sum of terms divided by number of terms
Mean= 10+5+8+10+12+6+8+10+15+6+12+18 ÷ 12
Mean = 120 ÷ 12 = 10
For finding the Median, first we need to rearrange the data in ascending order
5 6 6 8 8 10 10 10 12 12 15 18
We can see that the middle values are 10 and 10. So, the median will be the average of those two middle values.
Median = 10+10 ÷ 2
Median = 20 ÷ 2 = 10
From the calculation, we can see that both the median and mean are equal so, the data is symmetrical
25 pts Maureen tracks the range of outdoor temperatures over three days. She records the following information.
(picture attached)
Which answer below expresses the intersection of the three days as an inequality in terms of temperature, t. (The Intersection would be the temperatures they have in common.)
0 < t < 40
0 ≤ t ≤ 40
-23 ≤ t ≤ 50
-23 < t < 50
Answers
Answer: 0 ≤ t ≤ 40
Step-by-step explanation:
0 and 40 are included in all 3 number lines.
Thelma and Laura start a lawn-mowing business and buy a lawnmower for $225. They plan to charge $15 to mow one lawn. They would like to earn a profit of at least $750
Part A: Define a variable to represent the unknown quantity in this situation.
Part B: Write an inequality to represent the amount of money charged per lawn, the cost of the lawnmower and the profit.
Answers
Answer:
I got 65
Step-by-step explanation:
The profit will be given as:
P=$15x−$225
(where we subtracted the cost of the mower) so that P=$750
x will be the required number of needed lawns.
We need to solve:
$750=$15x−$225
rearranging:
x=$750+$225 / $15 =65 lawns
Define a variable and write an inequality to represent earning a specific profit in a lawn-mowing business.
Define variable:
Let x represent the number of lawns mowed.
Write inequality:
The inequality is 15x - 225 ≥ 750, where 15x is the amount earned, 225 is the cost of the lawnmower, and 750 is the desired profit.
Please help me please !!
Answers
Answer:
Acute
Step-by-step explanation:
7² + 9² ? 11²
49 + 81 ? 121
130 is greater than 121, so it is an acute triangle
NEED ANSWERED ASAP WILL REWARD BRAINLIEST
Pick method (1) or (2) to find the partial sum of the first 100 terms for this sequence.
1. Use the explicit formula, an = a1 + (n-1) d to find the 100th term for this sequence. Then use the partial sum formula sn = n/2 (a1 + an) formula to find s100.
2. Use technology (https://www.desmos.com/calculator) to find s100 using sigma notation with the explicit formula.
∑100n=1(a1 +(n−1)d)
EXPLAIN which method you used, show or explain what you did and remember to give your answer too.
Answers
Answer:
The sum of the first 100 terms is 60400
Step-by-step explanation:
* Lets revise the arithmetic sequence
- There is a constant difference between each two consecutive
numbers
- Ex:
# 2 , 5 , 8 , 11 , ……………………….
# 5 , 10 , 15 , 20 , …………………………
# 12 , 10 , 8 , 6 , ……………………………
* General term (nth term) of an Arithmetic sequence:
- U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d
- Un = a + (n – 1)d, where a is the first term , d is the difference
between each two consecutive terms n is the position of the
number
- The sum of first n terms of an Arithmetic sequence is calculate from
Sn = n/2[a + l], where a is the first term and l is the last term
* Now lets solve the problem
- We will use method (1)
- From the table the terms of the sequence are:
10 , 22 , 34 , 46 , 58 , 82 , 94 , ............., where 10 is the first term
∵ an = a1 + (n - 1) d ⇒ explicit formula
∵ a1 = 10 and a2 = 22
∵ d = a2 - a1
∴ d = 22 - 10 = 12
- The 100th term means the term of n = 100
∴ a100 = 10 + (100 - 1) 12
∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198
∴ The 100th term is 1198
- Lets find the sum of the first 100 terms of the sequence
∵ Sn = n/2[a1 + an]
∵ n = 100 , a = 10 , a100 = 1198
∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400
* The sum of the first 100 terms is 60400