Three Consecutive Numbers

The three consecutive numbers in different patterns are explained here.

(i) The sum of any three consecutive numbers is three times of the middle number:

1 + 2 + 3 = 6 = 3 x 2

2 + 3 + 4 = 9 = 3 x 3

7 + 8 + 9 = 24 = 3 x 8

24 + 25 + 26 = 75 = 3 x 25

37 + 38 + 39 = 114 = 3 x 38


(ii) The sum of any four consecutive numbers is twice the sum of two middle numbers:

1 + 2 + 3 + 4 = 10 = 2 (2 + 3) = 2 x 5

2 + 3 + 4 + 5 = 14 = 2 (3 + 4) = 2 x 7

5 + 6 + 7 + 8 = 26 = 2 (6 + 7) = 2 x 13

17 + 18 + 19 + 20 = 74 = 2 (18 + 19) = 2 x 37

40 + 41 + 42 + 43 = 166 = 2 (41 + 42) = 2 x 83


(iii) The sum of any five consecutive numbers is five times the exact middle number:

1 + 2 + 3 + 4 + 5 = 15 = 5 x 3 = (5 x 6)/2

2 + 3 + 4 + 5 + 6 = 20 = 5 x 4 = (6 x 7)/2 – 1

3 + 4 + 5 + 6 + 7 = 25 = 5 x 5 = (7 x 8)/2 - (1 + 2)

18 + 19 + 20 + 21 + 22 = 100 = 5 x 20 = (22 x 23)/2 – (17 x 18)/2

33 + 34 + 35 + 36 + 37 = 175 = 5 x 35

110 + 111 + 112 + 113 + 114 = 560 = 5 x 112


(iv) The same pattern may be seen in the sum of six, seven, eight, ……, etc, consecutive numbers.



Related Concept

Patterns and Mental Mathematics

Counting Numbers in Proper Pattern

Odd Numbers Patterns

Three Consecutive Numbers

Number Formed by Any Power

Product of The Number

Magic Square

Square of a Number

Difference of The Squares

Multiplied by Itself

Puzzle

Patterns

Systems of Numeration






4th Grade Math Activities

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