Question

Assertion (A): In an AP, the first term is 6, the last term is 78 and the sum of the given terms is 630. Then, there are 16 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 in an AP then $$S_{n} = \frac{n}{2} (a + l).$$

Options

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

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

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

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

Answer 1

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

Explanation:

Step 1 – Assertion: A is false. Using the stated sum formula, $$630 = \frac{n}{2}(6 + 78) = 42n,$$ so $$n = 15,$$ not 16.

Step 2 – Reason: R is true. It gives the sum formula for an AP when the first and last terms are known.