Power based series are formed via mathematical operations relating to the powers of numbers.

**The rule of increasing increments or decreasing decrements (IIDD)**

The rule says, if the consecutive difference between terms in the series **increases at an increasing rate or decreases at a decreasing rate**, there is high likelihood power based algebra is at play in it.

Here is an example:

2, 9, 28, 65, 126 ?

A] 217

B] 201

C] 343

D] 320

E] 253

The difference between consecutive terms is increasing at an increasing rate 7, 19, 37, 61. Hence the series cannot be a simple difference based series or a difference based series which increases by a constant rate. By now, we should also have checked for pair based matching and used the 1, 2, 3 rule of interleaved series. When all the above techniques do not yield a clue, it is helpful to turn our attention to a power based rule.

(Do give this problem a shot before proceeding ahead!)

Solution

**Solution – A] 217**. The square of numbers is 1,4,9,25…doesn’t look similar to the series given to us. The cube of numbers is 1, 8, 27, 64,125… aha seems very similar!

The series comprises of the cube of ascending number plus 1(1^{3}+1, 2^{3}+1, 3^{3}+1, 4^{3}+1…).

The next number in the series is 6^{3}+1

It is super handy to memorize the squares and cubes of common numbers

Power based series usually come along with one or two other rules such as pair matching, interleaving in the form of compound series in the IPAT. We cover this format of question extensively in our IPAT practice book which you can get here.