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# 10, 17, 26, 37, ? Complete the series

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Current Student
Joined: 25 Apr 2017
Posts: 46
GMAT 1: 700 Q49 V35
WE: General Management (Education)
Re: 10, 17, 26, 37, ? Complete the series  [#permalink]

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10 Jul 2017, 08:20
Going by this pattern of 3x3+1, 4x4+1, 5x5+1, 6x6+1, next numbers should be 50, 65, 82, 101 and so on.

Is this correct?
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7236
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: 10, 17, 26, 37, ? Complete the series  [#permalink]

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12 Jul 2017, 11:59
enzoeducation wrote:
10, 17, 26, 37, ? Complete the series

To find any formular and to complete a sequance, those works are very impirical.

The differences between adjacent terms are 7 (=17-10), 9 (=26-17) and 11 (=37-26).
Thus the following differences could be 13, 15, 17, 19 and so on.
Rest of terms would be 50, 65, 82, 101 and so on.

How can we derive its formula?

We have following conditions.

a_1 = 10
a_n+1 = a_n + 2n +5
We can verify that a_2 = a_1 + 2*1 + 5, a_3 = a_2 + 2*2 + 5 and so on.

Then we have following equations.

a_1 = 10
a_2 = a_1 + 2*1 + 5
a_3 = a_2 + 2*2 + 5
.
.
.
a_n = a_n-1 + 2*(n-1) + 5

After making sum of all above equation, we have a_n = 2*1 + 2*2 + ... + c*(n-1) + 10 + 5*(n-1) = 2*n(n-1)/2 + 10 + 5*(n-1) = n^2 + 4n + 5 = (n+2)^2 + 1.
We have the formula of n-th term, (n+2)^2 + 1.

Happy Studying !!!
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Re: 10, 17, 26, 37, ? Complete the series   [#permalink] 12 Jul 2017, 11:59
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# 10, 17, 26, 37, ? Complete the series

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