Answer:
A formula for the nth term of the given sequence is:
[tex]a_n=36\left(-\frac{4}{3}\right)^{n-1}[/tex]
Step-by-step explanation:
Given the sequence
36, -48, 64...
We know that a geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
Compute the ratios of all the adjacent terms
[tex]\frac{-48}{36}=-\frac{4}{3},\:\quad \frac{64}{-48}=-\frac{4}{3}[/tex]
The ratio of all the adjacent terms is the same and equal to
[tex]r=-\frac{4}{3}[/tex]
Therefore, the given sequence is a geometric sequence.
As the first element of the sequence is
[tex]a_1=36[/tex]
so substituting [tex]a_1=36[/tex] and [tex]r=-\frac{4}{3}[/tex] in the nth term
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=36\left(-\frac{4}{3}\right)^{n-1}[/tex]
Therefore, a formula for the nth term of the given sequence is:
[tex]a_n=36\left(-\frac{4}{3}\right)^{n-1}[/tex]
