Question

How many first odd natural numbers do we need to add together to get the number $81?$

• A. $8$
• B. $7$
• C. $10$
• D. $9$

Answer 1

The correct option is D $9$

$\bullet$ Sum of first $2$ odd natural numbers $=1+3=4=2^2$
$\bullet$ Sum of first $3$ odd natural numbers $=1+3+5=9=3^2$
$\bullet$ Sum of first $4$ odd natural numbers $=1+3+5+7=16=4^2$
$.$
$.$
$.$

Hence, we can conclude:

Sum of first $n$ odd natural numbers equals to $n^2.$

So, the sum of first $9$ odd natural numbers $=9^2=9\times 9=81$
$\Rightarrow$ $1+3+5+7+9+11+13+15+17=81$

Therefore, we need to add first $9$ odd natural numbers to get the sum value as $81.$

$\therefore$ Option (d.) is the correct answer.