Question

Assertion (A): The 10th term from the end of the AP 16, 11, 6, 1, ..., –79 is –34.

Reason (R): The nth term from the end of an AP with last term $$l$$ and common difference d is $${\{l - (n - 1)d}\}.$$

पर्याय

• 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 common difference is $$d = 11 - 16 = -5$$ and the last term is $$l = -79$$. Thus, the 10th term from the end is $$l - (10 - 1)d = -79 - 9(-5) = -34.$$

Step 2 – Reason: R is true. It gives the formula for the nth term from the end of an AP.

Step 3 – Link: Substituting the given last term, common difference and position into this formula gives $$-34$$, so R correctly explains A.