Question

Assertion (A)
If the first term of an AP is 6, last term is 62 and the sum of the given terms is 510. Then, there are 14 terms in the given AP.

Reason (R)
If a is the first term, l is the last term and n is the number of terms of an AP, then $S_n=\frac{n}{2}(a+1).$

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Answer 1

(d) Assertion (A) is false and Reason (R) is true.

The Reason (R) is clearly true.

$$\begin{gathered} \mathrm{Now},\frac{n}{2}\left(a+l\right)=510 \\ \Rightarrow \frac{n}{2}\left(6+62\right)=510 \\ \Rightarrow n=\frac{510}{34}=15 \end{gathered}$$

Thus, Assertion (A) is false.