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In the sequence An, A1=1，A2=2, and An+2=An+1+An+An-1+….+

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by Max@Math Revolution » Sun Jun 02, 2019 11:30 pm

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Answers

A

B

C

D

E

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Difficulty—

[GMAT math practice question]

In the sequence An, A1=1，A2=2, and An+2=An+1+An+An-1+....+A2+A1. What is the value of A14 / A12?

A. 1/4
B. 1/2
C. 1
D. 2
E. 4
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by Max@Math Revolution » Wed Jun 05, 2019 12:50 am
=>

A3 = A1 + A2
A4 = A1 + A2 + A3 = A3 + A3 = 2A3
A5 = A1 + A2 + A3 + A4 = A4 + A4 = 2A4
...
A13 = A1 + A2 + A3 + ... + A11 + A12 = A12 + A12 = 2A12
A14 = A1 + A2 + A3 + ... + A12 + A13 = A13 + A13 = 2A13 = 2(2A12) = 4A12

Thus A14 / A12 = 4

Therefore, E is the answer.
Answer: E
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