Question

Without adding, find the sum:
(i) (1 + 3 + 5 + 7 + 9 + 11 + 13)
(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

Sum of first n odd numbers $=n^2$

(i) $(1+3+5+7+9+11+13)=7^2=49$

(ii) $(1+3+5+7+9+11+13+15+17+19)={10}^2=100$

(iii) $(1+3+5+7+9+11+13+15+17+19+21+23)={12}^2=144$