# math

Nth expression for the following:6,11,17,24,32.....

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1. 41 it goes up a number each time

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2. The numbers represent the following sequence

n........1...2...3...4...4...
.........6..11..17..24..32...
1st diff...5...6...7...8
2nd dif......1...1...1

With the 2nd differences equal to 1, the general form of the equation defining the Nth term is a quadratic of the form N = an^2 + bn + c. Using the given data we can write

1 + b + c = 6
4a + 2b + c = 11
9a + 3b + c = 17

Solving yields a = 1/2, b 7/2 and c = 2 making the general expression for the Nth term N = (n^2 + 7n + 4)/2.

Thus, the sequence continues as
6, 11, 17, 24, 32, 41, 51, 62, 74...

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