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In the sequence {An}, A1=1 and An=An-1+ …. +A1. What is th

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by Max@Math Revolution » Thu May 31, 2018 3:28 am
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[GMAT math practice question]

In the sequence {An}, A1=1 and An=An-1+ …. +A1. What is the ratio of A12 to A10?

A. 1 to 1
B. 2 to 1
C. 4 to 1
D. 8 to 1
E. 16 to 1
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by GMATGuruNY » Thu May 31, 2018 4:49 am
To avoid confusion, the GMAT would probably rephrase the prompt along the following lines:
Max@Math Revolution wrote:[GMAT math practice question]

In the sequence {An}, each term after the first two terms is such that An = An-1+ …. +A1. If A1=1 and A2= 2, what is the ratio of A12 to A10?

A. 1 to 1
B. 2 to 1
C. 4 to 1
D. 8 to 1
E. 16 to 1
Each term after the first two terms is equal to the sum of the preceding terms:
A₃ = 2 + 1 = 3.
A₄ = 3 + 2 + 1 = 6.
A₅ = 6 + 3 + 2 + 1 = 12.
A₆ = 12 + 6 + 3 + 2 + 1 = 24.

The results above indicate that each term after the first two terms is twice the preceding term.
Thus:
A�� = 2A�₀
A�₂ = 2A�� = 2(2A�₀) = 4A�₀.

Since A�₂ = 4A�₀, we get;
A�₂/A�₀ = 4/1.

The correct answer is C.
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by Max@Math Revolution » Mon Jun 04, 2018 10:31 am
=>

Now,
A10 = A9 + … + A1.
So,
A11 = A10 + (A9 + … + A1) = A10 + A10 = 2A10
And
A12 = A11 + (A10 + … + A1) = A11 + A11 = 2A11 = 2*2A10 = 4A10.
Thus, the ratio of A12 to A10 is 4 to 1.

Therefore, the answer is C.
Answer : C
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