What is the 32nd term of the arithmetic sequence where a1 = −33 and a9 = −121? −396 −385 −374 −363

The formula to find the general term of an arithmetic sequence is,

Where = nth term and

= First term.

Given, a9 = −121. Therefore, we can set up an equation as following:

Since, a1 = -33

- 33 + 8d = -121

-33 + 8d + 33 = -121 + 33 Add 33 to each sides of the equation.

8d = -88.

Divide each sides by 8.

So, d = - 11.

Now to find the 32nd terms, plug in n = 32, a1 = -33 and d = -11 in the above formula. So,

= -33 + 31 ( -11)

= - 33 - 341

= -374

So, 32nd term = - 374.

Hope this helps you!

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