Question

Assertion: If T_n = 3n + 7 for a progression, then T₅ = 22.

Reason: The n^th term of AP = a + (n − 1)d.

Options

• Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Explanation:

The Assertion is true because when you put n = 5 into the formula T_n = 3n + 7, you get 3(5) + 7 = 22 through simple calculation. The Reason is also a true mathematical fact because a + (n − 1)d is indeed the standard formula for any Arithmetic Progression. However, you don’t actually need the A.P. formula from the Reason to prove the Assertion; you only need to substitute the number 5 into the given equation. Since the Assertion is solved by direct substitution and not by applying the general A.P. formula, the Reason does not explain the Assertion.