Question:
(i) Express 81 as the sum of 9 odd numbers.
(ii) Express 100 as the sum of 10 odd numbers.
Solution:
Sum of first $\mathrm{n}$ odd natural numbers $=n^{2}$
(i) Expressing 81 as a sum of 9 odd numbers:
$81=(9)^{2}$
$n=9$
$81=1+3+5+7+9+11+13+15+17$
(ii) Expressing 100 as a sum of 10 odd numbers:
$100=(10)^{2}$
$n=10$
$100=1+3+5+7+9+11+13+15+17+19$