Number Series – I

Test
Materials

Some standard patterns of series

Addition or Subtraction: Some number (or pattern of numbers) may be added or subtracted in each term to get the next term.

Example 1: Find the next term: 3, 6, 9, 12, 15, ?

Solution: This is very simple pattern. You can easily find that 33 is added to each term , and we are getting next term.

3 + 3 = 6

6 + 3 = 9

9 + 3 = 12

Similarly, 15 + 3 = 18. So, 18 will the next term. 

Example 2: Complete the following series: 4, 6, 9, 13, 18, ?

Solution: Pattern used in series:

4 + 2 = 6

6 + 3 = 9

9 + 4 = 13

13 + 5 = 18

Therefore, 18 + 6 = 2418+6=24“> So, 24 will be next term.

Example 3: Find the next term of series. 13, 11, 9, 7, 5, ?

Solution: As this is decreasing pattern, you can easily find that 22 is subtracted from each term to get the next term.

13 — 2 = 11

11 — 2 = 9

9 — 2 = 7

Similarly, 5 — 2 = 3. So, 33 will be the last term.

Multiplication or Division: Another pattern may be related to multiplication or division of some number to each term to get the next term.

Example 4: Find the next term 4, 8, 24, 96, ?

Solution: A particular pattern of numbers is multiplied to each term of series.

4 × 2 = 8

8 × 3 = 24

24 × 4 = 96

So, 96 × 5 = 480. 

Squaring or cubing: Another rules may be of squaring or cubing of the terms of series.

Example 5: Complete the following series 4, 9, 16, 25, ?

Solution: This is a very simple pattern i.e. a square of some pattern of numbers.

22 = 4

32 = 9

42 = 16

52 = 25

Continuing, 62 = 36.

Example 6: Complete the following series: 1, 27, 125, 343, ?

Solution: The series is based on following pattern:

13 = 1

33 = 27

53 = 125

73 = 343

Continuing, 93 = 729.

Mixed Patterns

Example 7: Find the next term of following series: 1, 2, 6, 21, 88, ?

Solution: Study this series, you will find out that more than one rule is applied on it. Following pattern is used in it: 1 × 1 + 1 = 22 × 2 + 2 = 66 × 3 + 3 = 2121 × 4 + 4 = 88 Series (1, 2, 3….) multiplied to term and then same series is added to get the next term. Therefore, 88 × 5 + 5 = 445.