Question

Assertion (A): The sum of first n terms of the A.P. –1, 5, 11 .... is \(3n^{2} - 4n\).

Reason (R): The sum of first n terms of an A.P. is given by \(\mathrm{S}_{n} = \frac{n}{2}[2a + (n - 1)d]\).

Options

• Both A and R are true, and R is the correct explanation of A.

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

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct explanation of A.

Explanation:

Assertion: Here \(a = -1\), \(d = 5 - (-1) = 6\), so \(S_n = \frac{n}{2}[2(-1) + (n - 1)6] = \frac{n}{2}(6n - 8) = 3n^{2} - 4n\). Hence A is true.

Reason: The formula \(\mathrm{S}_{n} = \frac{n}{2}[2a + (n - 1)d]\) is the standard sum formula and its direct application yields \(3n^{2} - 4n\), so R is true and correctly explains A.