Question

Find out the wrong number in the series 1,2,6,15,32,56,92

Answer 1

Answer:

Input : N = 8

Output : 141

Input : N = 20

Output : 2471

Approach:

The given series is:

1, 2, 6, 15, 31, 56, 92, 141, ...

First consecutive difference:

1 4 9 16 25 36 49 .......

Second consecutive difference:

3 5 7 9 11 13......

As the second consecutive difference is in AP, the nth term (tn) of the series is of the form,

A(n – 1)(n – 2)(n – 3) + B(n – 1)(n – 2) + C(n – 1) + D

So, tn = A(n – 1)(n – 2)(n – 3) + B(n – 1)(n – 2) + C(n – 1) + D

Now,

t1 = D = 1

t2 = C (2 – 1) + D = 2

t3 = 2B + 2C + D = 6

t4 = CA + 6B + 3C + D = 15

On solving the above four equations we get => A = 1/3, B = 3/2, C = 1, D = 1. On substituting these values tn and after simplifying we get,

t_{n} = \frac{2n^{3}-3n^{2}+n+6}{6}