### 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.

• ### 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)

• ### 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, ....)

• ### 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).

• ### 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....}

• ### 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,....}

• ### 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.)

• ### 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 ..}

• ### 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, ...}

• ### 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...}

### 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)}

• ### 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}

• ### 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...}

• ### 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)}

• ### 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..}

• ### 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....}

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