Question

Assertion (A): If the sum of first n terms of an A.P. is given \(\mathrm{S}_{n} = 2n^{2} - n\), then, its nth term is \(4n - 3\).

Reason (R): The nth term of an AP from the end is \(l - (n - 1)d\).

विकल्प

• 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, but R is not the correct explanation of A.

Explanation:

Assertion: \(T_n = S_n - S_{n - 1} = (2n^{2} - n) - (2n^{2} - 5n + 3) = 4n - 3\). Hence A is true. 

Reason: \(l-(n-1)d\) nth term from the end is a true statement, but it does not explain how the nth term is obtained from \(S_n\); hence R is not the correct explanation of A.