Let’s observe carefully the below written interesting pattern.
2² = 4 = 1 + 3
3² = 9 = 1 + 3 + 5
4² = 16 = 1 + 3 + 5 + 7
5² = 25 = 1 + 3 + 5 + 7 +9
6² = 36 = 1 + 3 + 5 + 7 + 9 + 11
7² = 49 = 1 + 3 + 5 + 7 + 9 + 11 + 13
8² = 64 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
9² = 81 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17
10² = 100 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
11² = 121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21
12² = 144 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
13² = 169 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25
14² = 196 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27
15² = 225 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29
Note:- The sum of n consecutive odd numbers yields n² , where n is a non-zero number. For example, sum of three consecutive odd numbers yields 3² (1 + 3 + 5 = 9) and sum of 12 consecutive odd numbers yields 12².
HAPPY LEARNING………………………