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Type of Series - Product Series

Posted on - 16-04-2017

Reasoning Series

Bank PO

Product Series:

A product series is usually a number series where the terms are obtained by a process of multiplication. Here also, there can be different types of series. We will look at these through examples. .

Consider the series 2, 4, 8, 16, 32, 64,………………. .

*2 *2 *2 *2 *2

2, 4, 8, 16, 32, 6

Here, each number in the series is multiplied by 2 to get the next term. So, the term that comes after 64 is 128. So, each term is multiplied by a fixed number to get the next term. Similarly we can have a series where we have numbers obtained by dividing the previous term with a constant number. For example, in the series 64, 32, 16,, 8, ....., each number is obtained by dividing the previous number by 2 (or in other words, by multiplying the previous term by '/2). So, here, the next term will be 4 (obtained by dividing 8 with 2). .

Consider the series 4, 20, 80, 240, ....

4, 20, 80, 240

x5 x4 x3

Here, the first term is multiplied by 5 to get the second term; the second term is multiplied by 4 to get the third term; the third term is multiplied by 3 to get the fourth term. Hence, to get the fifth term, we have to multiply the fourth term by 2, i.e., the fifth term is 480. So, each term is multiplied by a decreasing factor (or it could also be an increasing factor) to get the next term. That is, with whatever number a particular term is multiplied to get the next term, this latest term is multiplied by a number different from the previous multiplying factor to get the next term of the series. All the multiplying factors follow a certain pattern (normally of increasing or decreasing order). .

Consider the series 2, 6, 12, 20, 30,…..

2, 6, 12, 20, 30

+4 +6 +8 +10

This can be looked at a series of increasing differences. The differences of consecutive pairs of terms are 4 (between 2 and 6), 6 (between 6 and 12), 8 (between 12 and 20), 10 (between 20 and 30) and so on. Hence, the difference between 30 and the next term should be 12 and so the next term will be 42. But this series can also be looked at as a product series. .

2, 6, 12, 20, 30

1 x 2 2x3 3x4 4 x 5 5 x 6

The first term is the product of 1 and 2; the second term is the product of 2 and 3; the third term is the product of 3 and 4; the fourth term is the product of 4 and 5; the fifth term is the product of 5 and 6. Hence, the next term will be the product of 6 and 7 that is 42. .

 
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