I swear, last question!

Question

Calculate S(31) for the arithmetic sequence in which a(9) = 17 and the common difference is d = -2.1

-46
-29.2
32.7
71.3

Usually, I can figure these out but I'm stuck:(

Answer 1

a(n) = a(1) + (n-1)d
a(9) = a(1) + (9-1)d

You have a(9), you have d
Use those to get a(1) from the above mentioned.

Then, plug those values into the sum formula I mentioned on the other question.

Answer 2

Ok, I'm so sorry, but I got so lost.
For some reason, (I think) I'm getting it wrong at determining a(1).
I don't know what the heck I'm doing, but I've gotten either 5.9, -5.9, or 11.1 for a(1) and none of them work for the other formula. I feel super dumb right now, is there any chance you could show me again how to get a(1)? Sorry

Answer 3

Wait-- I made a dumb typo. I think it's 71.3 (oh my gosh I'm dying)

Answer 4

a(9) = a(1) + (n-1)d
a(9) = 17, d = -2.1

17 = a(1) + (9-1)*-2.1
a(1) = 17 + 16.8
= 33.8

S(31) = (n/2)[2a(1) + (n-1)d]
= (31/2)[2(33.8) + 30(-2.1)]
= (31/2)(67.6 - 63)
= (31/2)(4.6)
= 31*2.3
= 71.3

Yes, you're correct