Question

What is the 32nd term of the arithmetic sequence where a1 = -32 and a9 = -120? Choose one answer. A) -384. B) -373. C) -362. D) -351

Answer 1

Explanation:

Alright, lets get started.

The formula for nth term of arithmetic sequence is :

`t_(n)=a+(n-1)d`

First term is -32

Ninth term is :

`t_(9)=-32 + (9-1)*d`

`-120=-32+8*d`

`8d=-120+32`

`8d=-88`

`d=-11`

32th term is :

`t_(32)=-32 + (32-1)*(-11)`

`t_(32)=-32-341`

`t_(32)=-373`

So the answer is -373 : Answer

Hope it will help :)

Answer 2

a 1 = - 32, a 9 = - 120
a 9 = a 1 + 8 d
- 120 = - 32 + 8 d
8 d = - 88
d = - 88 : 8
d = - 11
a 32 = a 1 + 31 d = - 32 + 31 * ( -11 ) = - 32 - 341 = - 373
Answer: B ) - 373