Question

The start of an arithmetic sequence is 4, 11, 18, … One of the terms in the sequence has a value of 620. At what position in the sequence is this term?

Answer 1

Position 89.

Explanation:

Lets find the formula for the nth term of this sequence:

first term, a1 = 4.

Common difference, d = 11-4 = 18-11 = 7.

Term in position n:

nth term:

an = a1 + d(n - 1)

= 4 + 7(n - 1)

= 7n - 3.

Consider the term whose value is 620:

an = 620 = 7n - 3

7n = 620 + 3

7n = 623

n = 623/7

= 89.