Table of contents  
Number Series Formulas  
Formulas for Number Series  
Types of number series  
Square up and Square Add up Series 
A number series is a progression of numbers arranged based on a specific system or rule, without adhering to a particular order. The task involves identifying the underlying system or rule governing a given series and using it to determine the subsequent numbers.
For Example : 3, 9, 27, 81 ?
It is Geometric series.
Each term is Multiplied by 3.
So , 81 x 3 = 243
Types of Number Series is given below:
Add up Series +
These problems are never asked they are very easy, we are talking about them to introduce the number series from basic.
Add up Series –
Square up +(Easy to Identify)
Square up Add up +(Hard to Identify)
Square up Step up +(Very hard to identify not asked mostly unless paper is very tough)
Same for Step up Series +, but instead of adding, Subtract.
Example 1: Find the missing number? 99, 121, 143, ___, 187, 199 .
(a) 170
(b) 165
(c) 158
(d) 172
Ans: (b)
The given series is an AP with first term as 99 and common difference as 22.
Example 2: Find the next term in the series : 51,52,53,55,58,63,____.
(a) 69
(b) 77
(c) 81
(d) 71
Ans: (d)
Fibonacci series is added to each term.
51 + 0 =51
51 + 1=52
52 + 1=53
53 + 2=55
55 + 3=58
58 + 5=63
63 + 8=71
Example 3: Find the missing terms? 97,122,107,132,__,__.
(a) 117,142
(b) 122,112
(c) 141,131
(d) 121,131
Ans: (a)
This series is a result of alternate +25 and 15.
97 + 25=122
122 – 15=107
107 + 25=132
132 – 15=117
117 + 25=142
So, the next two terms are 117 and 142.
Example 4: Fill the missing term in the series
100, 92, 86 ,82, 74, 68, 64, 56, 50, __, ___.
(a) 44, 36
(b) 40, 34
(c) 46, 38
(d) 44, 32
Ans: (c)
The number series are in successive subtraction series of – 8, 6, 4 and then again 8,6,4.
So, the next terms after 50 will be 504=46 and 468=38.
Example 5: Select the missing number from the given responses.
19, 35, 67, 131, 259, 515, ?
(a) 1281
(b) 1291
(c) 1071
(d) 1027
Ans: (d)
11 × 2 – 3 = 19
19 × 2 – 3 = 35
35 × 2 – 3 = 67
67 × 2 – 3 = 131
131 × 2 – 3 = 259
259 × 2 – 3 = 515
515× 2 – 3 = 1027
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314 videos170 docs185 tests


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