Verified Solution • 2025–26 Session moderate

QJEEM20Ma9af4: JEE Main 2020 Mathematics - Class 11 JEEM20Ma9af4 Solution: Let , , ,....... be a G.P. such that < 0, + = 4 and + = 16. If…

Let a1{a_1} , a2{a_2} , a3{a_3} ,....... be a G.P. such that
a1{a_1} < 0, a1{a_1} + a2{a_2} = 4 and a3{a_3} + a4{a_4} = 16.
If ∑i=19ai=4λ\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda , then λ\lambda is equal to:

Multiple Choice Options

  • A 171
  • B -171
  • C -513
  • D 5113{{511} \over 3}

Step-by-Step Verified Solution

a1{a_1} + a2{a_2} = 4

⇒\Rightarrow a1{a_1} + a1{a_1} r = 4 ...(1)

a3{a_3} + a4{a_4} = 16

⇒\Rightarrow a1{a_1} r2 + a1{a_1} r3 = 16 ...(2)

Doing (1) ÷\div (2), we get

r = ±\pm 2

If r = 2, then a1 = 43{4 \over 3}

If r = -2, then a1 = -4

Given a1{a_1} < 0

∴\therefore a1 = -4

∴\therefore ∑i=19ai\sum\limits_{i = 1}^9 {{a_i}} = a(r9−1)r−1{{a\left( {{r^9} - 1} \right)} \over {r - 1}} = 4 λ\lambda

⇒\Rightarrow −4((−2)9−1)−2−1{{ - 4\left( {{{\left( { - 2} \right)}^9} - 1} \right)} \over { - 2 - 1}} = 4 λ\lambda

⇒\Rightarrow λ\lambda = -171

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring