Question

Assertion (A): In an AP, it is given that $$T_{9} = 39$$ and $$T_{15} = 63.$$ Then, its first term is 7 and the common difference is 4.

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 given terms imply $$a + 8d = 39$$ and $$a + 14d = 63.$$ Subtracting gives $$6d = 24,$$ so $$d = 4$$ and then $$a = 7.$$

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

Step 3 – Link: Using the nth-term formula for both given terms gives the equations that determine $$a = 7$$ and $$d = 4,$$ so R correctly explains A.