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ans E... two methods... 1) the eqn gives us (n-2)^2+(n+1)^2=(n+4)^2, which gives us on simplificstion n^2-10n-11=0... so n=11 or -1.. given that n is positive, 11 is the ans.. 2) second method.. the given equation basically are three sides of right angle triangle with hypotenuse on right side.. even number can be ruled out as ans.. since even^2+odd^2 can not be even^2.. in odd numbers only 11 satisfies the values for a right angle triangle 9,12 and 15.. as 9^2+12^2=15^2
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chetan2u found the "secret" to this question - while the prompt is based in Algebra, the 'shortcut' is actually based in Geometry (specifically a multiple of the 3/4/5 right triangle). You do not need to find the shortcut to answer this question though, if you know your Perfect Squares and how to do basic arithmetic.

The notation in the prompt tells us that each term in the sequence is equal to the "number" of the term squared.

Re: In the sequence a1,a2,…,an,…, an=n2 for all n>0. For what positive int [#permalink]

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02 Feb 2015, 22:26

Bunuel wrote:

In the sequence a1, a2, …, an, …, \(a_n=n^2\) for all n>0. For what positive integer n does \(a_{n-2}+a_{n+1}=a_{n+4}\)?

A. 7 B. 8 C. 9 D. 10 E. 11

Kudos for a correct solution.

Just expanding both sides we get (n-2)^2 + (n+1)^2 = (n+4)^2 Expanding and cancelling terms we get n^2-10n-11 = 0 Or (n-11)(n+1) = 0 So n=11 or -1. Since n is positive, n=11.

Re: In the sequence a1,a2,…,an,…, an=n2 for all n>0. For what positive int [#permalink]

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06 Oct 2017, 23:14

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