Question

In the arithmetic sequence −18,−12,−6 , . . . , which term is 54?

Answer 1

To find which term in the given arithmetic sequence is 54, we first need to find the common difference of the sequence.

Starting with the first term -18 and second term -12, we subtract -18 from -12 to get the common difference:
-12 - (-18) = 6

Therefore, the common difference of this arithmetic sequence is 6.

Next, we need to find out how many steps of the common difference of 6 it takes to reach the term 54. Starting from the first term -18, we can write a general formula for the nth term of the sequence:

An = a1 + (n-1)d

where An is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.

Plugging in the values we already know:
54 = -18 + (n-1)6
54 = -18 + 6n - 6
54 = -24 + 6n
78 = 6n
n = 13

Therefore, the 13th term in the given arithmetic sequence is 54.