Question

Find the missing number in the series: 2, 3, 5, 16, 231, ‘?'

Answer 1

53105

2^2 - 1^2 =3
3^2 - 2^2 =5
5^2 - 3^2 =16
16^2-5^2 =231
231^2-16^2=53105

Answer 2

The missing number in the series is 53105.

Given:

The series  2, 3, 5, 16, 231, ‘?'

To Find:

We have to find the missing number in the series: 2, 3, 5, 16, 231, ‘?'

Solution:

This is a problem for the series.

Let us tackle the problem.

We can easily solve this problem as follows,

The series  is 2, 3, 5, 16, 231, ‘?'

Let us assume the missing number is x.

We can easily see that,

$x_{i+1} ^{2} - x_{i}^{2} =x_{i+2}$

⇒$3^{2}-2^{2} =5$

$5^{2} -3^{2} =16$

$16^{2}-5^{2} =231$

Therefore,

$231^{2} - 16^{2} =53105$

Hence, the missing number in the series is 53105.

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