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If 10^(n)+3*4^(n+2) + k is divisible by...

If `10^(n)+3*4^(n+2) + k` is divisible by `9`, for all `ninN`, then the least positive integral value of `k` is

A

5

B

3

C

7

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Let P(n) : `10^(n)+3*4^(n+2)` + is divisible by 9, for all `ninN`. For n=1, the given statement is also true `10^(1)+3*4^(1+2)+k` is divisible by 9.
`because=10+3*64+k=10+192+k`
=202+k
If (202+k) is divisible by 9, then the least value of k must be 5.
`because` 202+5+207 is divisible by 9
`rArr(207)/(9)=23`
Hence, the least value of k is 5.
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