Odd Numbers

If continued odd numbers (starting from 1) are added, the sum is equal to the square* of the number of odd-numbers.

(i) 1 + 3 = 4 = 2 x 2 = 22

(ii) 1+3 + 5 = 9 = 3 x 3 = 32

(iii) 1 +3 + 5 + 7 = 16 = 4 x 4 = 42

(iv) 1 + 3 + 5 + 7 + 9 +11 = 36 = 6 x 6 = 62

…... and so on.


(a) The sum of first 10 odd numbers = 102 = 100

(b) The sum of first 15 odd numbers = 152 = 225

(c) The sum of first 19 odd numbers = 192 = 361

(d) The sum of first 21 odd numbers = 212 = 441

(e) The sum of first 26 odd numbers = 262 = 676



On the basis of the above facts regarding odd numbers, questions like these may be asked:

How many first odd numbers may give the sum 289?


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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