Question

* 1,5,14,30,55,91 __? *
A) 121
B) 136
C) 142
D) 140​

Answer 1

Required Answer:-

Here we have a number series with some numbers and we have to determine the next number following the same logic. Let's see the logic first:

$\LARGE{\underline{ \bf{ \red{Logic:}}}}$

The series is increasing unevenly. Once observe the difference of the consecutive terms. (2nd - 1st, 3rd - 2nd and so on.....)

• 5 - 1 = 4 = 2²
• 14 - 5 = 9 = 3²
• 30 - 14 = 16 = 4²
• 55 - 30 = 25 = 5²
• 91 - 55 = 36 = 6²

The differences between the numbers are consecutive perfect squares starting from 2. The next difference will be 7² i.e. 49.

Hence:-

The next term should be 91 + 49 = 140 (D)

Answer 2

Answer:

Given :-

A series of 1,5,14,30,55,91

To Find :-

The next number

Knowledge Required :-

Here, firstly we will subtract the next number by before one then a square digit will formed and the squared number will be increasing by 1.

Let's Solve

$\sf \mapsto \: 5 - 1 = 4 = \sqrt{4} = \bold{{2}^{2} }$

$\sf \mapsto \: 14 - 5 = 9 = \sqrt{9} = \bold {{3}^{2} }$

$\sf \mapsto \: 30 - 14 = 16 = \sqrt{16} = \bold { {4}^{2} }$

$\sf \mapsto \: 55 - 30 = 25 = \sqrt{25} = \bold { {5}^{2} }$

$\sf \mapsto \: 91 - 55 = 36 = \sqrt{36} = \bold{ {6}^{2} }$

Similarly,

$\sf \mapsto \: 140 - 91 = 49 = \sqrt{49} = 7$

$\frak \red{140}$

Hence :-

Option D is correct