# Number Series Tricks, Questions and Videos

## Geometric Progression (GP) / Geometric Series

A sequence of numbers is said to be in geometric progression (GP), if the ratio of two consecutive terms in the sequence is always the same and is called the common ratio. The nth term of a series is given by
an=a. rn−1
l=a. rN−1
Sn=a(rn−1)/(r−1)
SN=a(rN−1)/(r−1),r≠1

Where,
a = first term sn = Sum of first n terms
r = common ratio sN = Sum of all N terms of the series
l = last term

For examples
3, 15, 75, 375, ………. n common ratio = 5
2,6, 18, 54 ………. common ratio = 3

## Combination Series

This can be series combing different rules in a logical way.

(a) Series of perfect squares: For example 9, 25, 49, 81, 121………
The series can be represented by the mathematical expression f(x)=(1+2x)2
Where x = 1, 2, 3

(b) Series of perfect cubes : For example,
(i) 1, 27, 729, 19683……..
Can be represented by f(x)=(27)x−1
Where x=1,2,3,4

(ii) 1, 64, 373, 1000…
Can be represented by fx=[1+3(x−1)]3
Where x = 1, 2, 3, 4…..

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## 3 Responses to “Number Series Tricks, Questions and Videos”

1. Comment made by Sohan on Mar 20th 2019 at 12:32 am: Reply

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2. Comment made by Showkat Bashir on Dec 11th 2019 at 3:42 pm: Reply

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