What is the 32nd term of the arithmetic sequence where a1 = –31 and a9 = –119?

In order to solve for a nth term in an arithmetic sequence, we use the formula written as:

an = a1 + (n-1)d

where an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.

First, we need to calculate for d from the given values above.  
a1 = -31 and a17 = -119


an = a1 + (n-1)d
-119 = -31 + (9-1)d
d = -11

The 32nd term is calculated as follows:

a32 = a1 + (n-1)d
a32= -31 + (32-1)(-11)
a32 = -372

Definitely