What is the 32nd term of the arithmetic sequence where a₁ = -32 and a₉ = -120?
-384, -373, -362, -351

Solution:

For a given sequence in an arithmetic sequence with first term a₁ and common difference d, we have,

a_n = a₁ + (n -1)d

Given a₁ = -32 and a₉ = -120

a₉ = a₁ + (9 -1)d = -120

-32 + 8d = -120

d = (-120 + 32)/ 8

d = -11

a₃₂ = a₁ + (32 -1)d

a₃₂ = -32 + (31)(-11) = -32 - 341

a₃₂ = -373

Option (ii) is the answer.

What is the 32nd term of the arithmetic sequence where a₁ = -32 and a₉ = -120?

Summary:

The 32nd term of the arithmetic sequence where a₁ = -32 and a₉ = -120 is -373.