Question

Find the next three terms in the geometric sequence. 20 637 , - 1, 10 5 21) 72 V, V Vx

Answer 1

Given the geometric sequence:

`(20)/(63),-(10)/(21),(5)/(7),\ldots,\ldots,\ldots`

We need to find the next three terms of the geometric sequence

So, first, we will find the common ratio of the terms as follows

The common ratio = r =

`-(10)/(21)/(20)/(63)=-(10)/(21)*(63)/(20)=-(10)/(20)*(63)/(21)=-(1)/(2)*3=-(3)/(2)`

So, the common ratio = r = -3/2

The next three terms will be:

`\begin{gathered} -(3)/(2)*(5)/(7)=-(15)/(14) \\ \\ -(3)/(2)*-(15)/(14)=(45)/(28) \\ \\ -(3)/(2)*(45)/(28)=-(135)/(56) \end{gathered}`

So, the answer will be the terms are:

`-(15)/(14),(45)/(28),-(135)/(56)`