Question

Number series 1,3,9,31,?,651

Answer 1

the series is 1,3,9,31,129,651

Answer 2

The missing term is 129

Solution:

Given series is:

1 , 3, 9, 31, ? , 651

We have to find the missing term

Let us first analyse the series

$First\ term = 1\\\\second\ term = 1 \times 1 + 2 = 1 + 2 = 3\\\\Third\ term = 3 \times 2 + 3 = 6 + 3 = 9\\\\Fourth\ term = 9 \times 3 + 4 = 27 + 4 = 31\\\\Fifth\ term = 31 \times 4 + 5 = 124 + 5 = 129\\\\Sixth\ term = 129 \times 5 + 6 = 645 + 6 = 651$

Thus the logic used is:

$nth\ term =(n-1)th\ term \times (n-1) + n$

Thus the missing term is 129

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