# If $n$ is any natural number,

Question:

If $n$ is any natural number, then $6^{n}-5^{n}$ always ends with

(a) 1

(b) 3

(c) 5

(d) 7

[Hint: For any $n \in N, 6^{n}$ and $5^{n}$ end with 6 and 5 respectively. Therefore, $6^{n}-5^{n}$ always ends with $6-5=1$.]

Solution:

We know that $6^{n}$ will end in 6

And $5^{n}$ will end in 5 .

Now, $6^{n}-5^{n}$ always end with $6-5=1$

Hence the correct choice in (a).