Question

The sum of the first two terms of a GP is -4 and the fifth term is 4 times the third term.

1. Find the first term and the common ratio. 

2. Find the GP.

Answer 1

1. Given; S₂ = -4

a + ar = -4 ⇒ a(1 + r) = -4  .........(1)

Also given; t₅ = 4t₃ ⇒ ar⁴ = Aar²

⇒ r² = 4 ⇒ r = ±2

When r = 2(1) ⇒ a(1 + 2) = -4 ⇒ a = −43

When r = -2 (1) ⇒ a(1 – 2) = -4 ⇒ a = 4

2. When r= 2; GP is \(-\frac{4}{3}\),\(-\frac{8}{3}\),\(-\frac{16}{3}\),…

When r = – 2; GP is 4, -8, 16,…