## Life 2 years ago Write each arithmetic series as the sum of terms, find each sum.

1. Life

|dw:1354173691072:dw|

2. Life

this one's different

3. Life

how do i find a_1

4. Life

is it -5?

5. sagarrobo

|dw:1354173877445:dw| put k=10 and get answer

6. sagarrobo

7. Life

does a_1 =-5 ?

8. geoffb

\(a_1\) is the result of the equation when you plug your first term into it. Your equation is \(100-5k\). The series starts when k = 1, so plug 1 in for k and solve. That's \(a_1\).

9. sagarrobo

100-5k is general term for k series so first term=95

10. Life

11. Life

its wrong i know...

12. sagarrobo

its wrong refer to my solution above in figure

13. geoffb

@Life: You need to distinguish between the formula for the sum of the series and the equation you're given (in this case, 100-5k). You need to find the value for \(a_{10}\), and then plug that into your series summation formula.

14. geoffb

\(a_1 = 95\) (you solved that already). \(a_{n} = a_{10} = 100-5(10)\) Plug \(a_{1}\), \(a_{10}\) (which is the *value* you get—*not* 10), and \(n\) into your \(S_{n}\) formula and solve.

15. Life

i dont understand how "I" got 95, i never did, but i undetstand everything after that, i thought a1=-5

16. geoffb

Your equation is \(100-5k\), so \(a_{1}\) will be the result you get when you plug 1 in for \(k\).

17. geoffb

\(a_{2}\) will be the result you get when you plug in 2 for \(k\). \(a_{3}\) will be the result you get when you plug in 3 for \(k\). ... \(a_{10}\) will be the result you get when you plug in 10 for \(k\).

18. geoffb

@Life: Have you ever done computer programming? If so, do you know what a for loop is?

19. geoffb

That's all a series is. For each value from what's below sigma to what's above it (in this case, between k=1 and k=10), perform the equation. Once you know each one, add them all together.

20. Life

my final answer, s10=725, AM I RIGHT? :)

21. geoffb

Yes.

22. Life

sorry for being dumb lol, i understand it now though, so it was all worth it

23. geoffb

You're not being dumb. You are showing effort (not just "what's the answer?"), which is appreciated. :)

24. geoffb

Good luck with the rest of them. I have faith that you'll get them all. Good night. :)

25. Life

Good night :D

26. Life

I really do appreciate you sticking with me until i understood it. It was probably a good half an hour before I finally understood it, so thanks a bunch