The user-friendly version of this content is available here.

The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

This problem trains for: SAT-I, AMC-8, GMAT.

Given the sequence

equation

what is the rank of the smallest term that exceeds 167?

Notice that the sequence is arithmetic with first term 4 and common difference 9. The kth term can be written generically as:

equation

The smallest term that exceeds 167 is the smallest integer k that satisfies the inequality:

equation

Solve the inequality for k:

equation

equation

equation

equation

equation

and select the smallest integer that satisfies:

equation