Question

Assertion (A): The next term of the AP $$\sqrt{3},\ \sqrt{12},\ \sqrt{27},\ \ldots$$ is $$\sqrt{48}.$$

Reason (R): In an AP, we have $$T_{n + 1} = (T_{n} + d).$$

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 terms simplify to $$\sqrt{3}, 2\sqrt{3}, 3\sqrt{3},$$ so the common difference is $$\sqrt{3}$$ and the next term is $$4\sqrt{3} = \sqrt{48}.$$

Step 2 – Reason: R is true. In an AP, the next term is obtained by adding the common difference to the current term.

Step 3 – Link: Adding the common difference $$\sqrt{3}$$ to the third term $$3\sqrt{3}$$ gives $$4\sqrt{3} = \sqrt{48},$$ so R correctly explains A.