If 10^n + 3 4^ n+2 + is divisible by 9 for all n , then the least… - Vidyadip

MCQ

If $10^\text{n} + 3 \times 4^{\text{n}+2}+\lambda$ is divisible by $9$ for all $\text{n}\in\text{N},$ then the least positive integer value of $\lambda$ is

✓
$5$
B
$3$
C
$7$
D
$1$

✓

Answer

Correct option: A.

$5$

Given,
$10\text{n }+3\times^{\text{n}+2}+\lambda$ is divisible by $9,$
$\text{P}(1)=10^1+3\times4^{1+2}+\lambda$ is exactly divisible by $9$ then the value of $\lambda$ is $5$.

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