Question

Find the number of natural numbers lying between ${16}^2$ & ${17}^2$.

• A. $32$
• B. $35$
• C. $20$
• D. $27$

Answer 1

Answer: (A)

$32$

Natural numbers lying between ${16}^2$ and ${17}^2$ are ${16}^2+1,{16}^2+2,........,{17}^2-2,{17}^2-1$

which are in A.P. with common difference $1$

$\therefore$ Number of terms $=\frac{\text{Last term}-\text{First term}}{\text{Common difference}}+1$

$=\frac{({17}^2-1)-({16}^2+1)}{1}+1$

$=({17}^2-{16}^2)-2+1=(17+16)(17-16)-1=32\left(1\right)=32$

Hence, option A is correct.