Question

Assertion (A): 47 + 45 + 43 + ... + 11 is an AP having 19 terms.

Reason (R): In an AP with first term a and common difference d, the nth term is given by $$T_{n} = a + (n - 1)d.$$

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

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 sequence has first term $$a = 47$$, common difference $$d = -2$$ and last term $$T_{n} = 11$$. Using the nth-term formula, $$47 + (n - 1)(-2) = 11,$$ which gives $$n = 19.$$

Step 2 – Reason: R is true. It states the nth-term formula for an AP.

Step 3 – Link: Applying the formula to the first and last terms yields 19 terms, so R correctly explains A.