Question

Assertion: If S_n denotes the sum of n terms of an A.P., then S₁₂ = (S₈ − S₄).

Reason: For an A. P., `S_n = n/2[2a + (n - 1)d]`

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Explanation:

The Reason (R) is true because it gives the standard formula for the sum of n terms of an A.P. The Assertion (A) is considered true because when you substitute the formula from the Reason into the terms S₁₂, S₈, and S₄, and simplify the right-hand side, it mathematically proves the relationship S₁₂ = 3(S₈ − S₄).