Tip #1: Arithmetic Series, Geometric Series, Patterns in Differences

(1) Arithmetic Series: When the differences between the successive numbers given in the series is the same. For example: 2, 5, 8, 11, 14... (Here the difference between the numbers is 3, hence the next number will be 17)

(2) Geometric Series: When each successive number in the series is obtained by multiplying or dividing the previous one by a fixed number. For example: 2, 6, 18, 72,…

(3) Patterns in differences:Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.

Question: Look at this series: V, VIII, XI, XIV, __, XX, ... What number should fill the blank?

Solution:

This is an arithmetic series in Roman numerals; each no. is 3 more than the previous one. Thus, the missing number will be the Roman equivalent of 20 – 3 = 17, i.e., XVII.

Question: Look at this series: 201, 202, 204, 207, ... What number should come next?

Solution:

The difference between the successive numbers is 1, 2, 3 respectively. Thus, the difference keeps on increasing by 1. Thus, the next number in the series will be 207 + 4 = 211.

Tip #2: Pattern in Alternate/Adjacent numbers

1. Pattern in Alternate numbers: When there is a pattern between every alternate or third number in the series. For example: 2, 9, 5, 12, 8 , 15, 11....

2. (2) Pattern in adjacent number: When adjacent numbers in the series changes based on a logical pattern. For example: 2, 4, 12, 48... Here the numbers are being multiplied by 2, then by 3, then by 4 etc.

Question: Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?

Solution:

This is a complex series in which the successive letters decrease by 1 and the successive numbers are multiplied by 2. Thus, the number in the blank will be E4.

Question: Look carefully at the following series and choose the pair that comes next.

42 40 38 35 33 31 28

A. 25, 22 B. 26, 23 C. 26, 24 D. 25, 23

Solution:

This is an alternating subtraction series in which 2 is subtracted twice, then 3 is subtracted once, then 2 is subtracted twice, and so on. So the next terms in the following series will be 26 and 24. Thus the correct answer is C.

Tip #3: Prime Numbers, Squares/Cubes, Alternate primes/exponents

(1) Squares/Cubes: When numbers are a series of perfect squares. For example: 81, 100, 121, 144, 169...

(2) Cube/Square roots: When the numbers are a series of perfect cubes. For example: 512, 729, 1000...

(3) Alternate Primes: Here the series is framed by taking the alternative prime numbers. For example: 2, 5, 11, 17, 23, 31…

Question: Look at this series: 4, 7, 16, 13, __, 19, 64, 29, ... What number should fill the blank?

Solution:

There are two alternating series here. The first one is the square of the multiples of 2 {2^{2}, 4^{2}, 6^{2}, 8^{2} …} and the second one is a series of alternating prime numbers. The missing number is a part of the first series so the missing number is 6^{2} = 36.

Question: Look carefully at the following series and choose the pair that comes next.

4 7 26 10 13 20 16

A. 14, 17 B.18, 14 C. 19, 13 D.19, 14

Solution:

Two patterns alternate here, with every third number following the alternate pattern. In the main series, beginning with 4, 3 is added to each number to arrive at the next. In the alternating series, beginning with 26, 6 is subtracted from each number to arrive at the next. So the next numbers will be 16 + 3 = 19, 20 – 6 = 14. Thus, the correct answer is D.

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Number Series

Number Series: Find the missing number in the series, Number Series Questions with Tricks, Number Series Reasoning Questions with solved examples