•  Number Series With Common Difference

Identify the pattern

Identifying correct pattern is the key to apply a trick successfully. If you make mistake in identifying the pattern, you may calculate to wrong answer. Thus, request you to pay special attention in identifying the correct pattern

Pattern to apply this trick –

A + (A±x) + (A±2x) + (A±3x) + ……..

Where : x is any number

In this kind of number series , difference between any 2 consecutive number will be same

Example

1 + 5 + 9 + 13 + 17 => 1 + (1 + 4) + (1 + 2*4) + (1 + 3*4) ; Here common difference is 4
or
10 + 5 + 0 -5 -10 -15 => 10 + (10 – 5) + (10 – 2*5) + (10 – 3*5) + (10 – 4*5) + (10 – 5*5) ; Here common difference is -5
or
10 + 20 + 30 + 40 + 50 => 10 + (10 + 1*10) + (10 + 2*10) + (10 + 3*10) + (10 + 3*10) ; Here common difference is 10

All of these are example of adding number series with common difference. You can take any series and crosscheck to confirm that difference between any 2 consecutive number will be same.

Example : Take first series for crosscheck.
1 + 5 + 9 + 13 + 17
In this Series :
5-1 = 9-5 = 13-9 = 17-13 =4

Quick Answer Trick –

You may get a direct question of this kind in competitive exam or you may need to solve this kind of pattern as part of some other question. In both of these cases, solving this type of problem with trick is most time efficient. Remember time & accuracy is the key to crack a competitive exam.

Step 1. Count total numbers in the given number series. let’s say it is n.
Step 2. Identify first and last number in series. Let’s say it is f and l correspondingly.
Step 3. Answer = n(f+l)/2

Explanation with example :

Ex-1 : 1 + 5 + 9 + 13 + 17 = ?
Identify the pattern :
Given question is addition of number series with common difference (4)
Total numbers in the given number series : 5
first (f) and last (l) numbers are 1 and 17 correspondingly.
Answer = 5(1+17)/2 = 45

Ex-2 : 10 + 5 + 0 -5 -10 -15 = ?
Identify the pattern :
Given question is addition of number series with common difference (-5)
Total numbers in the given number series : 6
first (f) and last (l) numbers are 10 and -15 correspondingly.
Answer = 6(10 + -15)/2 = -15

Practice Questions:

Q1. 1 + 7 + 13 + 19 + 25 = ?

Q2. 22 + 27 + 32 + 37 = ?

Q3. 5 + 3 + 1 -1 – 3 -5 -7 -9 = ?

Q4. 105 + 110 + 115 + 120 + 125= ?

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