Question

2,3,7,16,32,57, ?

kindly explain this equation
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Answer 1

Answer:

16–7 =9

32–16 = 16

57–32 = 25

So the difference series is 1,4,9,16,25,……. which is the square of natural numbers

= 1^2,2^2,3^2,4^2,5^2,….

So the difference to the next number will be 6^2 = 36

So number is 57 + 36 = 93.

Answer is 93

Note : A generic equation for this series can be derived,

1st term = 2

2nd term = 2 + 1^2

3rd term = 2 + 1^2 + 2^2

nth term = 2 + 1^2 + 2^2 + 3^2 + … + (n-1)^2 ….

…… see equation for sum of squares for n terms

= 2 + (n(n-1)(2n-1) / 6)

For example , here 7th term has to found, there for

7th term = 2 + ((7*6*13)/6)

= 2 + (7*13) = 2 + 91 = 93

Hope it helped you

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