Number Series - Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems related to Number Series. Basic knowledge regarding solving number series questions is important for various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

Important Formulae and Tricks on Number Series

Below is Possible Types of Number Series

Type 1: Addition or Subtraction Series (Difference Series)

Case 1: Simple Addition or Subtraction ( + N/ -N) or Arithmetic Progression

In this type of series a number is incremented/ decremented by a fixed value.

Eg 1: 5, 9, 13, 17, 21,..... ( A number is incremented by 4)
Eg 2: 11, 17, 23, 29, 35....( A number is incremented by 6)
Eg 3: 349, 324, 299, 274, 249...... (A number is decremented by 25)

Case 2: Series Addition or Subtraction

In this type of series next number is incremented or decremented by an other series.

Eg 1: 2, 5, 9, 14, 20, 27, 35, .... (Number is incremented by 3, 4, 5, 6, 7....)
Eg 2: 13, 17, 25, 37, 53, ...... ( Number is incremented by 4, 8, 12, 16,...)
Eg 3: 841, 821, 796, 766, 731, ....( Number is decremented by 20, 25, 30, 35, ....)

Type 2: Multiplication or Division Series

Case 1: Simple Multiplication or Division (*N/ ÷N) or Geometrical Progression.

In this type of number series a number is either multiplied by a fixed number or divided by a fixed number.

Eg 1: 2, 6, 18, 54, 162, 486, 1454 .... (A number is multiplied by 3)
Eg 2: 6, 12, 24, 48, 96, 192, 384.......( A number is multiplied by 2)
Eg 3: 4096, 1024, 256, 64, 16, 4...... ( A number is divided by 4).

Case 2: Multiplication or Division by Arithmetic Series

In this type of series a number is multiplied or divided by an arithmetic series.

Eg 1: 1, 1, 2, 6, 24, 120, 720, .....{Numbers are multiplied by 1, 2, 3, 4, 5, 6, ....}
Eg 2: 5040, 720, 120, 24, .......{Numbers are divided by 7, 6, 5, 4....}

Case 3: Mixed multiplication or Division and Addition or Subtraction Series:

In this type of series a number is multiplied/ divided by a fixed number and other number is added/ subtracted to get next number of the series.

Eg 1: 1, 3, 7, 15, 31, 63, .... {Series is achieved by *2 +1}
Eg 2: 1, 2, 6, 21, 88, 445,....{Series is achieved by *1 +1, *2 +2, *3 + 3, ....}
Eg 3: 1, 4, 11, 26, 57, 120, ..{Series is achieved by *2+2, *2+3, *2+4,....}

Type 3: Prime Number Series: {A prime number has only two factors i.e 1 and the number itself}

Case 1: Simple prime number series:

This type of series is consecutive prime number series.

Eg 1: 3, 5, 7, 11, 13, 17.......(Given series is a consecutive prime number series)
Eg 2: 3, 5, 11, 19, 37,..........(Here 5 is first prime number after 3, 11 is second prime number after 5, 19 is third prime number after 11 and so on.)

Case 2: Prime number addition/ subtraction series:

In this type of series next number is addition or subtraction of prime number series.

Eg 1: 1, 4, 9, 16, 27, 40.... {Number is incremented by prime number series 3, 5, 7, 11, 13 .}
Eg 2: 234, 231, 226, 219, 208, ....{Number is decremented by prime number series 3, 5, 7, 11, 13 ..}

Case 3: Prime number multiplication and division series:

In this type of series next number is multiplication or division of prime number series.

Eg 1: 1, 3, 15, 105, 1155, 15015.... {Number is multiplied by prime number series. 3, 5, 7, 11, 13, ..}
Eg 2: 255255, 15015, 1155, 105, 15 ..... {Number is divided by prime number series. 17, 13, 11, 7, ...}

Type 4: N² series.

Case 1: Simple N² series

This type of series includes square of numbers.

Eg 1: 1, 4, 9, 16, 25, 36, 49...... { Numbers are square of 1, 2, 3, 4, 5, ...}
Eg 2: 1, 9, 25, 49, 81, ... { Numbers are squares of consecutive odd numbers 1, 3, 5, 7...}

Case 2: N² series with addition or subtraction

This type of series include N² series with addition or subtraction with fixed number or number series.

Eg 1: 2, 5, 10, 17, 26,.... {Series is (N² + 1)}
Eg 2: 0, 2, 6, 12, 20, .... {Series is (N² - N)}

Case 3: Addition or subtraction of N² series

In this type of series N² is either added or subtracted from a number to form the series

Eg 1: 154, 155, 164, 189, 238, 319,.. {1, 9, 25, 49... are added to form the series}
Eg 2: 884, 859, 823, 774, 710, ... {25, 36, 49, 64... are subtracted to form the series}

Type 5: N³ series.

Case 1: Simple N³ series

This type of series includes cubes of numbers.

Eg 1: 1, 8, 27, 64, 125, 216, 343...... { Numbers are cubes of 1, 2, 3, 4, 5, ...}
Eg 2: 4, 64, 216, 512,..., ... { Numbers are cubes of consecutive even numbers 2, 4, 6, 8...}

Case 2: N³ series with addition or subtraction

This type of series include N² series with addition or subtraction with fixed number or number series.

Eg 1: 0, 7, 26, 63, 124,.... {Series is (N³ - 1)}
Eg 2: 2, 10, 30, 68, 130, .... {Series is (N³ + N)}

Type 6: Miscellaneous Series

Case 1: Combination of two series:

When a series is combination of two series.

Eg 1: 1, 4, 4, 8, 7, 16, 10, 32, 13,... {This series is combination of two series: (i). 1, 4, 7, 10...., (ii). 4, 8, 16, 32....}
Eg 2: 42, 61, 45, 56, 48, 51, 51, 46, ..{ This series is combination of two series: (i). 42, 45, 48, 51.. (ii). 61, 56, 51, 46..}

Case II: Duel arithmetic operation series:

When more than one arithmetic operations are performed

Eg 1: 9, 27, 31, 155, 161, 1127, ..{The pattern is *3, +4, *5, +6, *7...}
Eg 2: 41, 43, 38, 40, 35, 37, 32, ...{ The pattern is +2, -5, +2, -5....}