Answer:
For the sequence is
,-4 ,-24 ,-144 ,...
Hence the formula
for x=1,2,3,... represents the given geometric sequence
Step-by-step explanation:
Given sequence is
,-4 ,-24 ,-144 ,...
To find the formula to describe the given sequence :
Let
,
,
,...
First find the common ratio
here
and,




here
and 



Therefore the common ratio is 6
Therefore the given sequence is geometric sequence
The nth term of the geometric sequence is

The formula which describes the given geometric sequence is
for x=1,2,3,...
for x=1,2,3,...
Now verify that
for x=1,2,3,... represents the given geometric sequence or not
put x=1 and the value of
in
for x=1,2,3,...
we get


Therefore 
put x=2 we get


Therefore 
put x=3 we get


Therefore 
Therefore the sequence is f(1),f(2),f(3),...
Therefore the sequence is
,-4 ,-24 ,-144 ,...
Hence the formula
for x=1,2,3,... represents the given geometric sequence is verified
Therefore the formula
for x=1,2,3,... represents the given geometric sequence