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The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4

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The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4  [#permalink]

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New post 11 Jul 2018, 01:12
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[GMAT math practice question]

The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 - A3 = 10. Which of the following could be the formula for An+1 - An, in terms of n?

\(A. n + 1\)
\(B. n^2 + 1\)
\(C. n^2 - 1\)
\(D. n - 1\)
\(E. n^2 + 3\)

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Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4  [#permalink]

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New post 11 Jul 2018, 02:01
Solving by substitution

Given \(A_{3}-A_{2} = 5\)

Above equation is of the form \(A_{n+1} - A_{n}\) with n = 2

Choice A = > \(n+1 = 2+1 = 3\neq5\) Wrong

Choice B = > \(n^2+1 = 4+1 = 5\neq5\) Probably correct

Choice C = > \(n^2-1 = 4-1 = 3\neq5\) Wrong

Choice D = > \(n-1 = 2-1 = 1\neq5\) Wrong

Choice E = > \(n^2+3 = 4+3 = 7\neq5\) Wrong


Hence option B
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Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4  [#permalink]

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New post 11 Jul 2018, 03:03
MathRevolution wrote:
[GMAT math practice question]

The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 - A3 = 10. Which of the following could be the formula for An+1 - An, in terms of n?

\(A. n + 1\)
\(B. n^2 + 1\)
\(C. n^2 - 1\)
\(D. n - 1\)
\(E. n^2 + 3\)


Let n=3.
According to the blue portion above, An+1 - An = A4 - A3 = 10.
The correct answer must yield a result of 10 when n=3.
Only B works:
n² + 1 = 3² + 1 = 10.


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Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4  [#permalink]

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New post 15 Jul 2018, 07:01
=>

We try each possibility until we find a formula that works.
A): If An+1 - An = n + 1, then A2 - A1 = \(1 + 1 = 2\), which is correct, but
A3 - A2 = \(2 + 1 = 3 ≠ 5.\)
So, A) is not the answer.
B): If An+1 - An = \(n^2 +\)1, then
A2 - A1 = \(1^2 + 1 = 2,\)
A3 - A2 =\(2^2 + 1 = 5,\)
A4 - A3 = \(3^2 + 1 = 10.\)
So, this formula is possible.

Therefore, the answer is B.
Answer: B
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Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 &nbs [#permalink] 15 Jul 2018, 07:01
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