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What is the last digit of 3^(3^(4n)) +1,...

What is the last digit of `3^(3^(4n)) +1`, where n is a natural number?

A

2

B

7

C

8

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
In `3^(n)`, last digit is 3, if n=1,9 if n=2,7 if n=3 and 1 if
n=4 and it is repeated after than
Given expression is `3^(3^(4n))+1`
Let `x=3^(3^(4n))+1=3^(8"In")+1`
`rArr" "x=3^(80n).3^(n)+1`
Last digit of x will be decided by `3^(n)" since "3^(80n)` has power multiple of 4.
If n=1 last digit is 3+1=4
n=2 last digit is `3^(2)+1=9+1=10`
So, last digit is zero.
n=3 last digit is `3^(3)+1=27+1=28`
last digit is 8.
If n=4 last digit is `3^(4)+1=81+1=82`
last digit is 2.
So, there is no definite value of last digit.
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