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

Given the sequence

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:

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

Solve the inequality for k:

and select the smallest integer that satisfies: