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

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

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To solve the ninth term in an arithmetic sequence, we use the formula written as:

an = a1 + (n-1) d

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

First, we need to calculate your d from the values ​​given 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