Question

Given the geometric sequence: -880, -220, -55,...
the next term in the sequence is?

Answer 1

The next term in the sequence is -13.75.

Answer 2

Answer: -13.75

Explanation:

In geometric sequence
`a , ar , ar^2 , ar^3` , where each term is given by :-

`T_n=ar^(n-1)` , where r= common ratio

a= first term.

n= Number of term

The given geometric sequence : -880, -220, -55,...

First term :
`a=-880`

Second term :
`ar=-220`

Now ,
`r=(ar)/(a)=(-220)/(-880)=(1)/(4)`

Now , the next term will be the 4th term , so for n=4 , we have

Fourth term =
`ar^(4-1)=ar^3`

Put value of a and r , we get

Fourth term =(-880)(\dfrac{1}{4})^3=\dfrac{-880}{64}=-13.75[/tex]

Hence, the next term in the sequence is -13.75 .