Question

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

Answer 1

An arithmetic sequence has a constant difference between two consecutive terms.
If the fisrt term is a1, and the nth term is an, then
a1 = a1
a2 = a1 + d
a3 = a2 + d = a1 + d + d = a1 + 2d
a4 = a3 + d = a1 + 2d + d = a1 + 3d
...
an = a1 + (n - 1)d

Answer 2

is there anything shorter?

Answer 3

You are given a1 and a27, and for a27, n = 27. Using the formula above, find d.
Then use the formula again using the d you found and n=42 to find a42.