Question

Assertion (A): For an A.P., \(\mathrm{T}_{22} = 149\) and \(d = 7\). Then \(\mathrm{S}_{22}\) is 1661.

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

पर्याय

• 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

A is true, but R is false.

Explanation:

Assertion: \(a + 21(7) = 149 \Rightarrow a = 2\), and \(S_{22} = \frac{22}{2}[2(2) + 21(7)] = 11(151) = 1661\). Hence A is true. 

Reason: The correct formula is \(\mathrm{S}_{n} = \frac{n}{2}[2a + (n - 1)d]\) with a plus sign; the reason has a minus sign, so R is false.