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?

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