What is the 32nd term of the arithmetic sequence where a₁ = 15 and a₁₃ = -57?

Solution:

Given, a₁ = 15

Also, a₁₃ = -57

The n-th term of an arithmetic sequence is given by a_n = a + (n - 1)d

So, a + (13 - 1)d = -57

15 + 12d = -57

12d = -57 -15

12d = -72

d = -6

Now find a₃₂

a₃₂ = a + (32 -1) × d

a₃₂ = 15 + 31 × (-6)

a₃₂ = 15 + (-186)

a₃₂ = -171

Therefore, the value of a₃₂ = -171.

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What is the 32nd term of the arithmetic sequence where a₁ = 15 and a₁₃ = -57?

Summary:

The 32nd term of the arithmetic sequence where a₁ = 15 and a₁₃ = -57 is a₃₂ = -171.