Assertion (A): P(n) = 7n - 3n is divisible by 4. Reason (R): If a ≠ b, then expansion an - bn is divisible by a - b if n is odd or even.

Question

Assertion (A): P(n) = 7n - 3n is divisible by 4. Reason (R): If a ≠ b, then expansion an - bn is divisible by a - b if n is odd or even. (A) Both (A) (R) are individually true (R) is correct explanation of (A). (B) Both (A) (R) are individually true but (R) is not the correct (proper) explanation of (A). (C) (A) is true but (R) is false. (D) (A) is false but (R) is true

Tardigrade Admin · Accepted Answer

P(n) = 7n - 3n, n is either even or odd, (a = 7, b = 3) is divisible by a - 6 = 7 - 3 = 4 Hence Assertion (A) followed by Reason (R).

Q. Assertion (A): $P (n) = 7^{n} - 3^{n}$ is divisible by $4$ .
Reason (R) : If $a \neq = b$ , then expansion $a^{n} - b^{n}$ is divisible by $a - b$ if n is odd or even.

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

(A) is true but (R) is false.

(A) is false but (R) is true

$P (n) = 7^{n} - 3^{n}, n$ is either even or odd, $(a = 7, b = 3)$ is divisible by $a - 6 = 7 - 3 = 4$ Hence Assertion $(A)$ followed by Reason $(R)$ .

Q. Assertion (A): P(n)=7n−3n is divisible by 4. Reason (R) : If a=b, then expansion an−bn is divisible by a−b if n is odd or even.