Question

Let a₁, a₂, a₃,… be a G.P. such that a₁ < 0, a₁ + a₂ = 4 and a₃ + a₄ = 16. If ∑a_i = 4λ, i ∈ [i = 1, 9], then λ is equal to :

(1) –171 

(2) 171

(3) 511/3

(4) -513

Comments

Answer is +171,because r<1 then the sum of n terms in G.P is different from what you used.
PLEASE REPLY ME,AM I WRONG OR RIGHT?

---

Here the formula used for the sum of G.P is correct for |r|>1

Answer 1

Answer is (1)

a₁ + a₂ = 4

r²a₁ + r²a₂ = 16

⇒ r² = 4 ⇒ r = –2 as a₁ < 0

and a₁ + a₂ = 4

a₁ + a₁(–2) = 4 ⇒  a₁ = –4

Answer 2

Answer is (1)

a₁ + a₂ = 4 ⇒ a₁ + a₁r = 4 ....(i)

a₃ + a₄ = 16 ⇒ a₁r² + a₁r² = 16 ...(ii)