The statement P(n) = 9n - 8n , when divided 8, always leaves the remainder

Question

The statement P(n) = 9n - 8n , when divided 8, always leaves the remainder (A) 2 (B) 3 (C) 1 (D) 7

Tardigrade Admin · Accepted Answer

P(n)=9n -8n P(1) = 9 - 8 = 1 P ( 1 )-1 = 0 which is divisible by 8 ∴ P(1) = 1 is the remainder, when P(n) is divided by 8. P(2) = 92 - 82 = 17 = 16 + 1 arrow remainder is 1, when divided by 8.

Q. The statement $P (n) = 9^{n} - 8^{n}$ , when divided 8, always leaves the remainder

2

3

1

7

$P (n) = 9^{n} - 8^{n}$
$P (1) = 9 - 8 = 1$
$P (1) - 1 = 0$ which is divisible by 8
$∴ P (1) = 1$ is the remainder, when $P (n)$ is divided by 8.
$P (2) = 9^{2} - 8^{2}$
= 17 = 16 + 1
$\to$ remainder is 1, when divided by 8.

Q. The statement P(n)=9n−8n , when divided 8, always leaves the remainder

2

3

1

7

P(n)=9n−8n P(1)=9−8=1 P(1)−1=0 which is divisible by 8 ∴P(1)=1 is the remainder, when P(n) is divided by 8. P(2)=92−82 = 17 = 16 + 1 → remainder is 1, when divided by 8.

Q. The statement $P (n) = 9^{n} - 8^{n}$ , when divided 8, always leaves the remainder

$P (n) = 9^{n} - 8^{n}$
$P (1) = 9 - 8 = 1$
$P (1) - 1 = 0$ which is divisible by 8
$∴ P (1) = 1$ is the remainder, when $P (n)$ is divided by 8.
$P (2) = 9^{2} - 8^{2}$
= 17 = 16 + 1
$\to$ remainder is 1, when divided by 8.