Identify the 42nd term of an arithmetic sequence where a₁ = -12 and a₂₇ = 66.

Solution:

Given, a₁ = -12 and a₂₇ = 66

We have to find the 42nd term of an arithmetic sequence.

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

So, a + (27 - 1) d = 66

-12 + 26 d = 66

26d = 66 + 12

26d = 78

d = 3

Now find a₄₂

a₄₂ = a + (42 -1) × d

a₄₂ = -12 + 41 × 3

a₄₂ = -12 + 123

a₄₂ = 111

Therefore, the value of a₄₂ = 111.

Identify the 42nd term of an arithmetic sequence where a₁ = -12 and a₂₇ = 66.

Summary:

The 42nd term of the arithmetic sequence where a₁ = -12 and a₂₇ = 66 is a₄₂ = 111.