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## anonymous one year ago what is a summation notation for the series? a. -5 +2+9+16+...+261+268 b. 500+490+480+...+20+10

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1. Mehek14

what do you think?

2. anonymous

i have no idea on how to do this

3. Jhannybean

Iwould start with b, seems a bit easier.

4. Jhannybean

This is what you call an arithmetic sequence, where you have a common difference between the numbers in a sequence. Can you spot what the difference is?

5. anonymous

it decreases by ten

6. Jhannybean

I've got to head off for a bit, I'll get someone on to help you @Michele_Laino please? Thank you !

7. Mehek14

yes it does decrease by 10 each time

8. Mehek14

how about in A?

9. anonymous

by 7?

10. Mehek14

increase or decrease

11. anonymous

increasing

12. Mehek14

correct

13. anonymous

what's next?

14. Loser66

For a) $$a_2= a_1+7\\a_3= a_2+7= a_1+2*7\\a_4=a_3+7 = a_1+3*7\\--------------\\a_n= a_1+(n-1)7$$

15. Loser66

Now, calculate the last term: $$268 = a_1 +(n-1) 7=-5 +(n-1) *7$$ solve for n, you have n= 40 Hence the summation is $\sum_{n=1}^{40} -5+7(n-1)$

16. Loser66

Imitate the same process to get the answer for b) instead of +7, you do -10

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