What is the 32nd term of the arithmetic sequence where a₁ = 13 and a₁₃ = -59?

Solution:

The nth term of an arithmetic sequence whose first term is a₁ and common difference is d is

a₁ + (n - 1) d

It is given that

a₁ = 13 and a₁₃ = -59

We know that

a₁₃ = a₁ + (13 - 1) d

13 + 12d = - 59

12d = -59 - 13

12d = -72

d = -72/12

d = -6

Now we have to find the 32nd term

a₃₂ = a₁ + (32 - 1) d

Substituting the values

a₃₂ = 13 + (31) (-6)

a₃₂ = 13 - 186

So we get

a₃₂ = -173

Therefore, the 32nd term is -173.

---

What is the 32nd term of the arithmetic sequence where a₁ = 13 and a₁₃ = -59?

Summary:

The 32nd term of the arithmetic sequence where a₁ = 13 and a₁₃ = -59 is -173.