## anonymous 4 years ago What is the sum of the arithmetic sequence 137, 125, 113 …, if there are 38 terms?

1. myininaya

Do you see that the numbers are increasing by 8?

2. anonymous

yes

3. anonymous

i would do it the old school way and keep subtracting 12 until you get 38 terms, then add lol

4. myininaya

$\sum_{i=0}^{37}(137+8i)=137+8(0)+\sum_{i=1}^{37}(137+8i)$ Now use $\sum_{i=1}^{n}i=\frac{n(n+1)}{2} \text{ and } \sum_{i=1}^{n}c=cn$

5. anonymous

Im still not getting the correct answer

6. Zarkon

whay are people using d=8

7. Zarkon

*why

8. anonymous

i dont know im gonna guess

9. anonymous

Whenever you need to find the sum of an arithmetic series use this formula: $\frac n 2 \left( 2a+ (n-1) \right)\times d) \tag{1}$ a= first term n= number of terms d= common difference Here, $$n= 38, a = 137$$ and $$d = -12$$. Substituting these in $$(1)$$, and assuming my algebra is right you answer should be $$-3230$$

10. anonymous

I know but the answer does not show up in the multiple choose

11. anonymous

@NatalieLove: Revert if you need help in proving that formula.

12. anonymous

We are doing the same steps the test its incorrect. It does not show up as a choose Thank You

13. anonymous

Glad to help :)

14. myininaya

omg lol I said increasing by 8 and then continue to think the thingy was increasing by 8 sometimes i wonder about myself lol