An A.P. with 3rd term = -8 and 9th term = 4. Assertion (A): Common difference = -2. Reason (R): If first term of the A.P. is a, then (a + 8d) - (a + 2d) = -8 - 4. 1. A is true, R is false. 2. Both A and R are false. 3. Both A and R are true and R is correct reason for A. 4. Both A and R are true and R is incorrect reason for A.

Given, in an A.P. 3rd term = -8 and 9th term = 4. Let a be the first term of the A.P. and d be the common difference. By formula : ⇒ an = a + (n - 1)d ⇒ a3 = a + (3 - 1)d ⇒ -8 = a + 2d .................(1) ⇒ a9 = a + (9 - 1)d ⇒ 4 = a + 8d .................(2) Subtracting equation (1) from (2), we get : ⇒ (a + 8d) - (a + 2d) = 4 - (-8) ⇒ a + 8d - a - 2d = 4 + 8 ⇒ 6d = 12 ⇒ d = ⇒ d = 2. According to assertion d = -2, which is incorrect. So, assertion (A) is false. From above calculation, we get : ⇒ (a + 8d) - (a + 2d) = 4 - (-8) ⇒ (a + 8d) - (a + 2d) = 12 According to reason, ⇒ (a + 8d) - (a + 2d) = -8 - 4 ⇒ (a + 8d) - (a + 2d) = -12, which is incorrect. So, reason (R) is false. Hence, option 2 is the correct option.

Mathematics

An A.P. with 3^rd term = -8 and 9^th term = 4.
Assertion (A): Common difference = -2.
Reason (R): If first term of the A.P. is a, then (a + 8d) - (a + 2d) = -8 - 4.
A is true, R is false.
Both A and R are false.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.

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