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