If the first term of an A . P . is 3 and the sum of its first 25 terms is equal to the sum of its next 15…

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P.is
  1. 16
  2. 15
  3. 14
  4. 17

Solution

Sum of first25 terms=sum of next 15 terms

S25=SNext 15

⇒S25+SNext 15=S40

⇒2×S25=S40

⇒2×2522×3+24d=4022×3+39d

⇒52×3+24d=42×3+39d

⇒30+120d=24+156d

⇒36d=6⇒d=16

 

 

Asked in: JEE Main 2020 (03 Sep Shift 1)

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