JEE Main20202 Sep 2020Evening ShiftMathematicsSequences and SeriesActual
If the sum of first 11 terms of an A.P. , a 1 , a 2 , a 3 … … is 0 a 1 ≠ 0 then the sum of the A.P a 1 , a 3 , a 5 , … . . a 23 is k a 1 where k is equal to
Options
- A- 121 10
- B121 10
- C72 5
- D- 72 5
Correct answer
D. - 72 5
Step-by-step solution
Let a 1 be the first term and d be the common difference of A . P . ∴ S 11 = 0   ⇒ 11 2 2 a 1 + 10 d = 0 ⇒   a 1 + 5 d = 0 Now a 1 + a 3 + a 5 + … . + a 23 = 12 2 2 a 1 + 12 - 1 2 d = 12 a 1 + 11 d = 12 a 1 - 11 a 1 5 = - 72 a 1 5