Question

The common ratio of a geometric sequence is 3/2. Find the first three terms if the fifth term is 1.​

Answer 1

Answer:

16/81, 8/27,and 4/9

Step-by-step explanation:

Given

Common ratio r = 3/2

Let the first term be 'a'.

Fifth term = a₅ = 1

We know that  

For the nth term in G.P with common ratio 'r' and the first term 'a' is

aₙ = arⁿ⁻¹

⇒a₅= 1

⇒ar⁵⁻¹ = 1

⇒ar⁴ = 1

⇒a(3/2)⁴ = 1

⇒a = 1 / (3/2)⁴

⇒a = 2⁴/3⁴ = 16/81

∴a = 16/81

The first three terms of G.P are a, ar and ar².

∴ a₁ = a =16/81

  a₂ = ar = (16/81)*(3/2) = 8/27

  a₃ = ar² = (16/81)*(3/2)² = (16/81)* (9/4) = 4/9