Tn = 4 - 2n is the nth term of an A.P. Assertion (A): This A.P. will have all terms negative after 2nd term. Reason (R): The common difference is negative. 1. Assertion (A) is true, but Reason (R) is false. 2. Assertion (A) is false, but Reason (R) is true. 3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A). 4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Mathematics

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Given, T_n = 4 - 2n

⇒ T₁ = 4 - 2 x 1

= 4 - 2 = 2

⇒ T₂ = 4 - 2 x 2

= 4 - 4 = 0

⇒ T₃ = 4 - 2 x 3

= 4 - 6 = -2

⇒ T₄ = 4 - 2 x 4

= 4 - 8 = -4

So, the sequence 2, 0, -2, -4, …………..

After 2nd term, this A.P. will have all terms negative.

So, assertion (A) is true.

Common difference, T_n - T_{n - 1}

= [4 - 2n] - [4 - 2(n - 1)]

= 4 - 2n - [4 - 2n + 2]

= 4 - 2n - 4 + 2n - 2

= -2.

So, reason (R) is true and reason (R) is the correct explanation of assertion (A).

Hence, option 3 is the correct option.

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