Question

The fourth term of GP whose first term is 2 is 54.find it's common ratio​

Answer 1

common ratio r = 3

Explanation:

the nth term of a GP is

`a_(n)` = a₁
`r^(n-1)`

a₁ is the first term, r the common ratio , n the term number

given

a₁ = 2 and a₄ = 54 , then

a₁
`r^(3)` = 54

2 r³ = 54 ( divide both sides by 2 )

r³ = 27 ( take cube root of both sides )

`\sqrt[3]{r^3}` =
`\sqrt[3]{27}` , that is

r = 3