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

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

by Max@Math Revolution » Tue Jul 10, 2018 11:58 pm
[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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by Vincen » Wed Jul 11, 2018 12:30 am
Hi.

This is my answer.

We have that $$A_2-A_1=2=1+1=1^2+1.$$ $$A_3-A_2=5=4+1=2^2+1.$$ $$A_4-A_3=10=9+1=3^2+1.$$ Accordingly with this, the formula could be: $$A_{n+1}-A_n=n^2+1.$$ So, the correct answer is the option B.

Also, we could try the other formulas and they won't be coherent with the given information.
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by GMATGuruNY » Wed Jul 11, 2018 1:54 am
Max@Math Revolution 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.

The correct answer is B.
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by Max@Math Revolution » Sun Jul 15, 2018 5:47 am
=>

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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