Respuesta :
Answer:
The formula that can be used to describe the given sequence is [tex]f(x)=-4(6)^{x-1}[/tex]
Step-by-step explanation:
Given : sequence -4, −24, −144,...
We have to find the formula that can be used to describe the given sequence -4, −24, −144,...
A geometric sequence is a sequence in which each higher term is multiplied by a constant number called common ratio.
Written as a, ar , ar², ar³., ....
and general term is calculated as [tex]a_n=ar^{n-1}[/tex]
Where a is first term and r is common ratio.
Consider the given sequence -4, −24, −144,...
We find the common ratio ,
[tex]a=-4, \\\\ar=-24,\\\\\ ar^2=-144[/tex]
Thus, common ratio is given as [tex]r=\frac{ar}{r}=\frac{-24}{-4}=6[/tex]
Thus, the given sequence is a geometric sequence.
The general term is given by [tex]a_n=ar^{n-1}[/tex]
Put a = -4 , r = 6
We have
[tex]a_n=-4(6)^{n-1}[/tex]
Thus, the formula that can be used to describe the given sequence is [tex]f(x)=-4(6)^{x-1}[/tex]
Answer:
[tex]f(x) = -4(6)^{x-1}[/tex]
Step-by-step explanation:
Given sequence,
-4, -24, -144, .....
Since,
[tex]\frac{-24}{-4}=\frac{-144}{-24}=.........=6[/tex]
Thus, the given sequence is the Geometric sequence having common ratio 6,
Since, the formula of nth term of a GP is,
[tex]a_n = ar^{n-1}[/tex]
Here, a = -4 ( first term ) and r = 6 ( common difference,
Let x represents the total number of terms,
And, f(x) represents the xth term,
Then the required formula would be,
[tex]f(x) = -4(6)^{x-1}[/tex]
