Question

The 6 term of a G.P is -2\27 and it's first term is 18.what is the common ratio​

Answer 1

r = -
`(1)/(3)`

Explanation:

The n th term of a GP is

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 18 and a₆ = -
`(2)/(27)` , then

18
`r^(5)` = -
`(2)/(27)` ( divide both sides by 18 )

`r^(5)` = -
`(1)/(243)` ( take the fifth root of both sides )

r =
`\sqrt[5]{-(1)/(243) }` = -
`(1)/(3)`