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# What is the 32nd term of the arithmetic sequence where a_{1} = 13 and a_{13} = -59?

**Solution:**

The nth term of an arithmetic sequence whose first term is a_{1} and common difference is d is

a_{1} + (n - 1) d

It is given that

a_{1} = 13 and a_{13} = -59

We know that

a_{13} = a_{1} + (13 - 1) d

13 + 12d = - 59

12d = -59 - 13

12d = -72

d = -72/12

d = -6

Now we have to find the 32nd term

a_{32} = a_{1} + (32 - 1) d

Substituting the values

a_{32} = 13 + (31) (-6)

a_{32} = 13 - 186

So we get

a_{32} = -173

Therefore, the 32nd term is -173.

## What is the 32nd term of the arithmetic sequence where a_{1 }= 13 and a_{13} = -59?

**Summary:**

The 32nd term of the arithmetic sequence where a_{1} = 13 and a_{13} = -59 is -173.

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