Question

What is the remainder when $9^1+9^2+9^3+....+9^8$ is divided by 6?

• A. 3
• B. 2
• C. 0
• D. 5

Answer 1

The correct option is A 3

We have,

$9^1+9^2+9^3+......+9^8$

Now, We can write,

$3^2+3^4+3^6+.....+3^{16}$

$\Rightarrow 3(3^1+3^3+3^5+.....+3^{15})$

Now, we can observe that,

$3^k=2m+1$For some positive integer. k and m.