Question

Find the missing term.


3, 12, 27, 48, 75, 108, ?


The answer is 147. But how the anawer came

Answer 1

3,12,27,48,75,108,?
Difference b/w 12 and 3 = 9
Difference b/w 27 and 12=15
Difference b/w 48 and 27 = 21
Difference b/w 75 and 48 = 27
Difference b/w 108 and 75=33
The difference increases by 6. So, difference b/w ? and 108 is 39.
So, next term according to this pattern will be 147.

Answer 2

Given :

A series ,

3, 12, 27, 48, 75, 108, ?

To find :

The value of the missing term.

Solution :

If we consider the difference between adjacent terms , that is ,

$12 - 3 = 9\\27 - 12 = 15 \\48 - 27 = 21\\75 - 48 = 27\\108 - 75 = 33$

We , see that the difference between the adjacent terms differ by 6.

Hence , we can infer that

         $x - 108 = 39$

Therefore,

               $x = 147$

Final answer :

Hence ,the missing term in the given series is 147.