C
generate the first few terms using the recursive formula
[tex]a_{2}[/tex] = - 7 × [tex]\frac{1}{3}[/tex] = - [tex]\frac{7}{3}[/tex]
[tex]a_{3}[/tex] = - [tex]\frac{7}{3}[/tex] × [tex]\frac{1}{3}[/tex] = - [tex]\frac{7}{9}[/tex]
[tex]a_{4}[/tex] = - [tex]\frac{7}{9}[/tex] × [tex]\frac{1}{3}[/tex] = - [tex]\frac{7}{27}[/tex]
r = [tex]a_{2}[/tex] / [tex]a_{1}[/tex] = [tex]\frac{1}{3}[/tex]
the n th term formula (explicit ) for a geometric sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex]r^{n-1}[/tex] = - 7([tex]\frac{1}{3}[/tex])^(n - 1)
Answer:
Option C
Step-by-step explanation:
Given is a geometric sequence.
The recursive formula is given as
[tex]a_n = \frac{1}{3} a_{n-1}[/tex]
Hence ratio of nth term to n-1th term
=[tex]\frac{a_n}{a_{n-1} } =\frac{1}{3}[/tex]
[tex]r=\frac{1}{3}[/tex]
I term = [tex]a_1=-7[/tex]
Hence explicit formula is
[tex]a_n = -7(\frac{1}{3} )^{n-1}[/tex]
Option C is right
