Which of the following recursive formulas represents the same geometric sequence as the formula an = 3 • 3n - 1?

A. an = 9 • an - 1
B. an = 3 • an - 1
C. an = 9 + an - 1
D. an = 3 + an - 1

Question

Which of the following recursive formulas represents the same geometric sequence as the formula an = 3 • 3n - 1?

 		A.	an = 9 • an - 1
 		B.	an = 3 • an - 1
 		C.	an = 9 + an - 1
 		D.	an = 3 + an - 1

holsteremission · Answer

I assume the formula is $a_n=3\times3^{n-1}$?

You can replace $n$ with $n-1$, which by the above definition means you have $a_{n-1}=3\times3^{n-2}$. Notice that this is equivalent to $a_{n-1}=\color{red}{3^{n-1}}$. Notice also that this red term is exactly a factor of the formula for $a_n$.