Question

Assertion (A): The sum of first n even natural numbers is n(n + 1).

Reason (R): The sum of n terms of an AP with first term a and last term $$l$$ is $$S_{n} = \frac{n}{2},(a + l).$$

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

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

Explanation:

Step 1 – Assertion: A is true. The first $$n$$ even natural numbers form an AP with first term $$2$$ and last term $$2n$$.

Step 2 – Reason: R is true. The sum of $$n$$ terms of an AP with first term $$a$$ and last term $$l$$ is $$S_{n} = \frac{n}{2}(a + l).$$

Step 3 – Link: Using the given sum formula, $$S_{n} = \frac{n}{2}(2 + 2n) = n(n + 1),$$ so R correctly explains A.