Question

Find the value of
(i) 1 + 3 + 5 = _____
(ii) 1 + 3 + 5 + 7 + 9 +11 = ________
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =_____

Answer 1

Sum of n consecutive odd integers starting from 1 is equal to $n^2$
$\left(i\right)1+3+5=3^2=9$
$\left(ii\right)1+3+5+7+9+11=6^2=36$
(iii) Sum of n consecutive odd integers starting from 1 is equal to $n^2$
Here the total number of consecutive odd integers is 9.
Thus, n = 9 and their sum is $9^2=81$.
(In fact: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81)