Do you get terrified by Number Series Questions?

‘Number Series’ or ‘number sequence’ is an integral part of Quantitative Aptitude Section in various competitive examinations like IBPS Bank exams, SSC, RAIL and so on. I’ve come across many students who get petrified by looking at questions on number series. Lack of confidence subdues their logical faculty to come up with the missing number or next number in a series of numbers that are seemingly complicated. They are unable to decipher the predefined rule behind the sequence of numbers given. Once the rule is determined it’s simple to find out the next term(s) or missing term(s) in a series. It becomes simpler to solve number series questions following a step by step approach.

Different Type of Number Series

A series can be created in numerous ways. An understanding of these various ways can help us in recognizing the pattern followed in the number series. So here we go with some standard series types-

Arithmetic Series – Difference between successive terms is fixed. Subsequent terms are obtained by either adding or subtracting a fixed number. For example,

2, 5, 8, 11, 14, 17,…..                                Common Difference = 3

32, 25, 18, 11, 4,…….      Common Difference = -7

Geometric Series – Each term of the series is obtained by multiplying (or dividing) the previous number by a fixed number. Hence the ratio between any 2 consecutive terms is same. For example,

3, 6, 12, 24, 48, 96…….       Common Ratio = 2

2048, 512, 128, 32…….       Common Ratio = 1/4

Arithmetico-Geometric Series –  Each term is first added (or subtracted) by a fixed number and then multiplied (or divided) by another number to obtain the subsequent term. For example,

4, 18, 60, 186….. => 4, (4+2)x3, (18+2)x3, (60+2)x3

Geometrico-Arithmetic Series – Each term is first multiplied (or divided) by a fixed number and then added (or subtracted) by another number to obtain the subsequent term.For example,

3, 10, 24, 52…… => 3, (3×2)+4, (10×2)+4, (24×2)+4,…..

Series of Squares, Cubes, etc. – Each term is square or cube or a higher power of the previous term. For example,

3, 9, 81, 6561….                                         Each term is obtained by squaring the previous number

2, 8, 512, ………                                        Each term is obtained by cubing the previous number

Some non-standard ways in which series can be created –

Series with subsequent Differences being in Arithmetic Progression (AP)

3, 7, 13, 21, 31, 43……         The differences in subsequent terms are 4, 6, 8, 10, 12…. which are in AP

Series with Differences in Differences being in AP

336, 210, 120, 60, 24, 6, 0,….         The difference being 126, 90, 60, 36, 18, 6

The differences between differences being 36, 30, 24, 18, 12,…. and so on, which are in AP

Inter-Mingled Series – In this case any two of the above series are mixed in one. For example,

1, 3, 5, 1, 9, -3, 13, -11, 17,….

Odd terms (1, 5, 9, 13, 17,….) of the series are in AP, whereas even terms (3, 1, -3, -11,…) are in geometrico-arithmetic series in which subsequent terms are obtained by multiplying the previous term by 2 and then subtracting 5.

This list is by no means exhaustive. There can be infinite ways to make a number series. It’s not possible to think or write about them here.

I got inspired to write this article after reading Series Chapter of the awesome book named Magical Book on Quicker Maths by M.Tyra. It can be a boon for any competitive exam aspirant. We’ll talk more about series in future. You can post any question related to number series as a comment below.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

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