Power based series

Power based series are formed via some sort of mathematical operation on the powers of numbers. As powers of numbers are part of a disproportionate number of series questions, it is important to devote some time understanding them.

The rule of increasing increments or decreasing decrements (IIDD)

While it may not be easy to spot a power based rule on the face of it, the rule – IIDD – may help in partially validating if it is a power based series. The rule says, if the consecutive difference between terms in the series increase at an increasing rate or decrease at a decreasing rate, there is high likelihood power based algebra is at play in it.

Here is a simple example –

2, 9, 28, 65, 126 ?

The difference between consecutive terms is increasing at a rapidly increasing rate 7, 19, 37, 61. Hence it cannot be a simple difference based series or even an increasing difference based series which increases by a constant rate. By now, you 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, turn your attention to a power based rule.

Let’s see, ( Do give this a shot before proceeding ahead!)

Solution

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(13+1, 23+1, 33+1, 43+1…).

As a handy, please try 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.

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