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
● Puzzle
● Patterns
4th Grade Math Activities
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