If a 1 , a 2 , a 3 , . . . . are in A.P. such that a 1 + a 7 + a 16 = 40 , then the sum of the first 15…

If a1,a2,a3,.... are in A.P. such that a1+a7+a16=40, then the sum of the first 15 terms of this A.P is:
  1. 280
  2. 120
  3. 150
  4. 200

Solution

Let the 1st terms of A.P. be 'a' and common difference 'd' .
Given  a1+a7+a16=40
⇒a+a+6d+a+15d=40
⇒a+7d=403 ….(1)
Sum of first 15 term
S15=152[2a+14d]
=152×2×403=200

Asked in: JEE Main 2019 (12 Apr Shift 2)

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