Question

If $n$ is any natural number, then $9^n-5^n$ may end with ___________.

• A. 3
• B. 6
• C. 5
• D. 8

Answer 1

The correct option is B 6

$9^1=9$
$9^2=81$
$9^3=729$
$9^4=6561$
$\therefore$ On generalising, $9^n$ ends with either 9 or 1.
Similarly, $5^n$ ends with only $5$.

When $9^n$ ends with 9, then $9^n-5^n$ ends with 4 as 9 - 5 = 4.
When $9^n$ ends with 1, then $9^n-5^n$ ends with 6.