JEE Main201912 Apr 2019Evening ShiftMathematicsSequences and SeriesActual

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 terms of this A.P is:

Options

A280
B120
C150
D200

Correct answer

D. 200

Step-by-step solution

Let the 1 st terms of A.P. be ' a ' and common difference ' d ' . Given   a 1 + a 7 + a 16 = 40 ⇒ a + a + 6 d + a + 15 d = 40 ⇒ a + 7 d = 40 3 ….(1) Sum of first 15 term S 15 = 15 2 [ 2 a + 14 d ] = 15 2 × 2 × 40 3 = 200

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