Question

Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule.

Answer 1

Given that the series is 1, 3, 9, 27, ............

The common ratio will be

$Common\text{ ratio=}\frac{2nd\text{ term}}{1st\text{ term}}=\frac{3}{1}=3$

So the common ratio is 3.

The explicit formula uses starting term and the recursive formula uses the previous term.

As

$\begin{gathered} Explicit\text{ form} \\ a_n=3^{n-1} \\ Recursive\text{ form} \\ a_n=a_{n-1}\times3 \end{gathered}$

These are the required forms.