If `10^n+3xx4^(n+2)+lambda` is divisible by 9 or all natural numbers, then the least positive integral value of `lambda` is
a. `5`
b. `3`
c. `7`
d. `1`

Explanation

Let P(n) : `10n+3×4^(n+2)+λ`
is divisible by 9, for all nϵN

For n = 1, the given
statement is also true
`10^1+3.4^(1+2)+λ `is divisibleby9

∵=`10+3.64+λ=10+192+λ
=202λ`

If `(202 + λ) `is divisible by 9, then the least value of k must be 5

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