Question

What is the sum of a 30-term arithmetic sequence where the first term is 74 and the last term is -100?

Answer 1

@aum

Answer 2

-468
-442
-416
-390

Answer 3

The common difference d is found as follows:
Let the first term be a.
74 = a .....................(1)
-100 = a + 29d........(2)
If you subtract equation (2) form equation (1), the a terms will cancel and you will have a third equation that you can solve to find the value of d.
The sum S of n terms of an arithmetic sequence is found from the formula:
\[S=\frac{n}{2}[2a+(n-1)d]\]
When you have found the value of d, just plug the d value and the value of n (n = 30 ) and a (a = 74 ) into the formula to find the required sum of the sequence.

Answer 4

subtract equation (2) from equation (1)*

Answer 5

howd you get 29 @kropot72

Answer 6

The first term in the sequence (74) stands alone. The other 29 terms in the sequence are each the result of adding multiples of the common difference to the first term. So the last term in the sequence, the thirtieth, is the first term plus 29 times the common difference.

Answer 7

ohh

Answer 8

Have you calculated the value of common difference d yet?

Answer 9

idk if im right but i got 3

Answer 10

What is the result when you subtract equation (2) from equation (1)?
74 = a .....................(1)
-100 = a + 29d........(2)

Answer 11

im so confused

Answer 12

74 - (-100) = a - a -29d ..........(3)
Now you need to simplify equation (3)

Answer 13

Taking the left hand side of equation (3), what is:
74 - (-100) = ?

Answer 14

174

Answer 15

Good work! Now looking at the right hand side of equation (3), what is:
a - a - 29d = ?

Answer 16

-29d

Answer 17

Correct again! So now we have this equation derived from equation (3):
174 = -29d ...........(4)
Now you can solve for d by dividing both sides of equation (4) by -29.

Answer 18

-6

Answer 19

Good work. So we now have d = -6, n = 30, and a = 74 to plug into the formula for the sum, giving:
\[S=\frac{30}{2}[(74\times2)+(29\times -6)]=you\ can\ calculate\]

Answer 20

-390

Answer 21

Good work! You are correct.

Answer 22

thanks

Answer 23

You're welcome :)