Question

Let $P\left(n\right)=3^{2n}\forall n\in N$, when divided by $8$ leaves the remainder

• A. $2$
• B. $1$
• C. $4$
• D. $7$

Answer 1

The correct option is B $1$

$P\left(n\right)=3^{2n}={(1+8)}^n$

$\Rightarrow P\left(n\right)=1+n_{C_1}8+n_{C_2}{8}^2+...+n_{C_n}{8}^n$

$\Rightarrow P\left(n\right)=1+8(n_{C_1}+n_{C_2}8+...+n_{C_n}{8}^{n-1})$

Therefore, the remainder is 1 when divided by 8.
Ans: B