What is the 32nd term of the arithmetic sequence where a1 = –33 and a9 = –121?

The 32nd term of arithmetic sequence is -374.

Step-by-step explanation:

Given : the arithmetic sequence where and

We have to find the 32nd term of the arithmetic sequence.

For the arithmetic sequence having first term 'a' and common difference 'd' the general term  is defined by

Thus, for the given arithmetic sequence, we have,

First term is -33

We can calculate the common difference by putting a = -33 in above, we have,

-33 + 8 d = -121

Solving for d, we have,

8d = -121 + 33

⇒ 8d = -88

⇒ d = - 11

Thus, the common difference is -11.

For 32nd term, Put a = -33  , d = -11 and n = 32 in

We have,

Simplify, we have,

Thus, the 32nd term of arithmetic sequence is -374.

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