Question

Without adding, find the sum of the following numbers
(i) 1 + 3 + 5 + 7 + 9 =
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 =
[3 marks]

Answer 1

The sum of first ‘n’ odd natural numbers is equal to ${\text{n}}^2$.

(i) $1+3+5+7+9=5^2=25$
[1 mark]

(ii) $1+3+5+7+9+11+13+15+17=9^2=81$
[1 mark]

(iii) $1+3+5+7+9+11+13+15+17+19+21+23+25$
$={13}^2=169$
[1 mark]