Question

Without adding, find the sum
(i) $1+3+5+7+9$
(ii) $1+3+5+7+9+11+13+15+17+19$
(iii) $1+3+5+7+9+11+13+15+17+19+21+23$

Answer 1

(i) $1+3+5+7+9$
Since, there are $5$ consecutive odd numbers, Thus, their sum = $5^2=25$
(ii) $1+3+5+7+9+11+13+15+17+19$
Since, there are $10$ consecutive odd numbers, Thus, their sum = ${10}^2=100$
(iii) $1+3+5+7+9+11+13+15+17+19+21+23$
Since, there are $12$ consecutive odd numbers, Thus, their sum = ${12}^2=144$.