Verified Solution • 2025–26 Session moderate

QJEEM19Ma3eac: JEE Main 2019 Mathematics - Class 11 JEEM19Ma3eac Solution: If a 1 , a 2 , a 3 , ..... are in A.P. such that a 1 + a 7 + a…

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 :

Multiple Choice Options

  • A 120
  • B 200
  • C 150
  • D 280

Step-by-Step Verified Solution

a1 + a7 + a16 = 40

a1+(a1+6d)+(a1+15d)=40{a_1} + \left( {{a_1} + 6d} \right) + ({a_1} + 15d) = 40

⇒3a1+21d=40\Rightarrow 3{a_1} + 21d = 40

⇒a1+7d=403\Rightarrow {a_1} + 7d = {{40} \over 3}

⇒a1+a2.......+a15=152[a1+a15]\Rightarrow {a_1} + {a_2}....... + {a_{15}} = {{15} \over 2}[{a_1} + {a_{15}}]

⇒152[a1+a1+14d]⇒15(a1+7d)=15×403=200\Rightarrow {{15} \over 2}[{a_1} + {a_1} + 14d] \Rightarrow 15({a_1} + 7d) = 15 \times {{40} \over 3} = 200

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