Important Formulas: Number Series | Quantitative Aptitude for SSC CGL PDF Download

Number Series Formulas

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

Formulas for Number Series

Types of number series

Types of Number Series is given below:

• Arithmetic Sequence: A sequence in which every term is created by adding or subtracting a definite number to the preceding number is an arithmetic sequence.
• Geometric Sequence: A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.
• Harmonic Sequences: A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.
• Fibonacci Numbers: Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. 

Add Up Series

Add up Series +

• Probability of asking – Very Low
• Difficulty – Low
• Reason – to Introduce Concept

These problems are never asked they are very easy, we are talking about them to introduce the number series from basic.

1. Rule – Just Add a number ‘N’ to the last number.
2. E.g. – 5, (5 + 3 = 8), (8 + 3 = 11), ( 11 + 3= 14) ….
3. Result –  5, 8, 11, 14, 17 ……..

Add up Series –

• Probability of asking – Very Low
• Difficulty – Low
• Reason – to Introduce Concept

1. Rule : Just Add a number ‘N’ to the last number.
2. E.g. : 4, (4 – 5 =  (-1)), (-1 -5 = -6), ( -6 – 5 = -11) ….
3. Result : 4, -1, -6, -11, -16 ……..

Square up and Square Add up Series

Square up and Square Add up Series +

Square up +(Easy to Identify)

1. Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a²
2. E.g. – 5
   • 5 + 2² = 5 + 4 = 9
   • 9 + 3² = 9 + 9 = 18
   • 18 + 4² = 18 + 16 = 34
   • 34 + 5² = 34 + 25 = 59
3. Result – 5, 9, 18, 34, 59 …..

Square up Add up +(Hard to Identify)

1. Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a² + b for b some pattern.
2. E.g. – 5
   • 5 + 2² + 3 = 5 + 4 + 3 = 12
   • 12 + 3² + 3 = 12 + 9 + 3 = 24
   • 24 + 4² + 3 = 24 + 16 + 3 = 43
   • 43 + 5² + 3 = 43 + 25 + 3 = 71
3. Result – 5, 12, 24, 43, 71 …..

Square up Step up +(Very hard to identify not asked mostly unless paper is very tough)

1. Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + katex is not defined + b for b some pattern.
2. E.g. – 5
   • 5 + katex is not defined + 3 = 5 + 4 + 3 = 12
   • 12 + katex is not defined + 8(3+5) = 12 + 9 + 8 = 29
   • 29 + katex is not defined +13(8+5) = 29 + 16 + 13 = 58
   • 58 + katex is not defined + 18(13+5) = 58 + 25 + 18 = 101
3. Result – 5, 12, 29, 58, 101 ..

Square up and Square Add Up Series -

Same for Step up Series +, but instead of adding, Subtract.

Examples of Number Series

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 50-4=46 and 46-8=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