Question

What is the 32nd term of the arithmetic sequence where a1 = −31 and a9 = −119? −372 −361 −350 −339?

Answer 1

The difference of the sequence is -11 so your answer is -372

Answer 2

The 32nd term of the arithmetic sequence is:

-372

Explanation:

We are given first term of the sequence as:

`a_1=-31`

We know that the nth term of a arithmetic sequence is given by the formula:

`a_n=a_1+(n-1)d`

where d is the common difference of the arithmetic sequence.

We are given,

`a_9=-119`

i.e.

`a_1+(9-1)d=-119\\\\\\i.e.\\\\\\-31+8d=-119\\\\\\8d=-119+31\\\\\\8d=-88\\\\i.e.\\\\\\d=-11`

Hence, the 32nd term is given by:

`a_(32)=-31+(32-1)* (-11)\\\\\\a_(32)=-372`

Hence, the answer is: -372