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{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i

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{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i  [#permalink]

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New post 30 Jan 2019, 02:24
1
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A
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C
D
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Difficulty:

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Question Stats:

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[GMAT math practice question]

{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what is the value of a7?

A. 10
B. 12
C. 14
D. 15
E. 16

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{an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i  [#permalink]

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New post 30 Jan 2019, 18:47
1
An+2 = An+1 + An
An = An+2 - An+1


A1 = 2
A2 = ?
A3 = ?
A4 = 2

Sum of A2 + A3 must be 2 when A2 = An. (An+2 = An4 = An+1 = An3 + An = A2)

Subtraction of A3 - A2 must be 2 when An = An1. ((An = An1 = 2) = (An+2 = An3) - (An+1 = An2))

I took the values 2 and 0.

Given that A1 = 2 is positive, then A2 has to be 0 and A3 has to be 2 so...

A1 = A3 - A2 = 2 - 0 = 2 = A1

After that just sum:

A5 = A3 + A4 = 4
A6 = A4 + A5 = 6
A7 = A5 + A6 = 10

A
Math Revolution GMAT Instructor
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Re: {an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i  [#permalink]

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New post 01 Feb 2019, 02:50
=>

a3 = a2 + a1 = a2 + 2.
a4 = a3 + a2 = a2 + (a2 + 2) = 2a2 + 2 = 2.
Thus, a2 = 0 and a3 = 2.
Therefore,
a5 = a4 + a3 = 2 + 2 = 4,
a6 = a5 + a4 = 4 + 2 = 6,
and
a7 = a6 + a5 = 6 + 4 = 10.

Therefore, the answer is A.
Answer: A
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Re: {an} is a sequence satisfying an+2 = an+1 + an. If a1 = a4 = 2, what i   [#permalink] 01 Feb 2019, 02:50
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