Question

Assertion (A): The sum of 14 terms of the AP 7 + 10 + 13 + ... is 375.

Reason (R): The sum of n terms of an AP with first term a and common difference d is given by $$S_{n} = \frac{n}{2} \cdot {\{2a + (n - 1)d}\}.$$

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

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

Explanation:

Step 1 – Assertion: A is false. Here, $$a = 7$$, $$d = 3$$ and $$n = 14$$. Therefore, $$S_{14} = \frac{14}{2}{2(7) + (14 - 1)(3)} = 7(14 + 39) = 371,$$ not 375.

Step 2 – Reason: R is true. It gives the sum formula for $$n$$ terms of an AP.