Question

(i) Express 81 as the sum of 9 odd numbers.
(ii) Express 100 as the sum of 10 odd numbers.

Answer 1

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

(i) Expressing 81 as a sum of 9 odd numbers:
$$\begin{gathered} 81={\left(9\right)}^2 \\ n=9 \\ 81=1+3+5+7+9+11+13+15+17 \end{gathered}$$

(ii) Expressing 100 as a sum of 10 odd numbers:
$$\begin{gathered} 100={\left(10\right)}^2 \\ n=10 \\ 100=1+3+5+7+9+11+13+15+17+19 \end{gathered}$$