Answer :
Answer:
The formula for the nth term of the sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
Step-by-step explanation:
Given the sequence
6, -6, 6, -6
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
Computing the ratios of all the terms of the adjacent terms
[tex]\frac{-6}{6}=-1,\:\quad \frac{6}{-6}=-1,\:\quad \frac{-6}{6}=-1[/tex]
The ratio of all the adjacent terms is the same and equal
so
r = -1
so substituting r = -1 and [tex]a_1=6[/tex] in the geometric sequence
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=6\left(-1\right)^{n-1}[/tex]
Thus, the formula for the nth term of the sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]