What is the sum of the arithmetic sequence 137, 125, 113 …, if there are 38 terms?

Question

myininaya · Answer

Do you see that the numbers are increasing by 8?

anonymous · Answer

yes

anonymous · Answer

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

myininaya · Answer

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

anonymous · Answer

Im still not getting the correct answer

zarkon · Answer

whay are people using d=8

zarkon · Answer

*why

anonymous · Answer

i dont know im gonna guess

anonymous · Answer

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 $

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Glad to help :)

myininaya · Answer

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