There is a sequence $A_n$ such that $A_1 = 2$ , $A_2 = 5$ , and $A_n = A_{n-1}/A_{n-2}$ , when $n$ is an integer greater than 2. What is the value of $A_{149}$ ?

Correct answer marked below

2.5

1/2

1/5

Correct

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Comments

KarlMay 8

This one looked scary at first but once I wrote out the first several terms a pattern jumped out. Classic GMAT trick where the sequence cycles.

KamilJun 20

Wait, I got the cycle but then I lost track of where A_149 lands. Do you count the position within the repeating block starting from A_1 or after?

ArchanaJul 6

Pretty challenging for a 655-705. The division A_{n-1}/A_{n-2} creates a repeating pattern of length 6, and 149 mod 6 is the key step.

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.

There is a sequence AnA_nAn​ such that A1=2A_1 = 2A1​=2, A2=5A_2 = 5A2​=5, and An=An−1/An−2A_n = A_{n-1}/A_{n-2}An​=An−1​/An−2​, when nnn is an integer greater than 2. What is the value of A149A_{149}A149​?