Question

f(1)=6 f(n) =1/3f(n-1)what are the first 5 terms?

Answer 1

$\begin{gathered} f(1)=6 \\ f(n)=\frac{1}{3}f(n-1) \end{gathered}$

f(n-1) is the term previous to n.

As you know the 1st term, use to find the 2nd term :

$\begin{gathered} f(2)=\frac{1}{3}f(2-1) \\ \\ f(2)=\frac{1}{3}f(1) \\ \\ f(2)=\frac{1}{3}(6) \\ \\ f(2)=2 \end{gathered}$

Use 2nd term to find the 3rd term:

$\begin{gathered} f(3)=\frac{1}{3}(2) \\ \\ f(3)=\frac{2}{3} \end{gathered}$

Use 3rd term to find 4th term:

$\begin{gathered} f(4)=\frac{1}{3}\cdot\frac{2}{3} \\ \\ f(4)=\frac{2}{9} \end{gathered}$

Use 4th term to find 5th term:

$\begin{gathered} f(5)=\frac{1}{3}\cdot\frac{2}{9} \\ \\ f(5)=\frac{2}{27} \end{gathered}$

Then, the correct answer is A. 6,2, 2/3, 2/9, 2/27