Question

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

Answer 1

Answer: -13.75

Step-by-step 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  , $r=\dfrac{ar}{a}=\dfrac{-220}{-880}=\dfrac{1}{4}$

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 .

Answer 2

The next term in the sequence is -13.75.