QJEEM16Ma7078: JEE Main 2016 Mathematics - Class 11 JEEM16Ma7078 Solution: Let a 1 , a 2 , a 3 , . . . . . . . , a n , . . . . . be in…

Question

Verified Solution • 2025–26 Session moderate

Let a₁, a₂, a₃, . . . . . . . , a_n, . . . . . be in A.P.

If a₃ + a₇ + a₁₁ + a₁₅ = 72,

then the sum of its first 17 terms is equal to :

Accepted Answer

As a₁ a₂ . . . . . a_n . . . . . are in A.P.

∴

a₃ + a₁₅ = a₇ + a₁₁ = a₁ + a₁₇

Given,

a₃ + a₇ + a₁₁ + a₁₅ + a₁₅ = 72

\Rightarrow

(a₃ + a₁₅) + (a₇ + a₁₁) = 72

\Rightarrow

2(a₁ + a₁₇) = 72

\Rightarrow

(a₁ + a₁₇) = 36

∴

Sum of first 17 terms

=

\frac{17}{2}

(a₁ + a₁₇)

=

\frac{17}{2}

\times

36

= 306

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