Question

3, -9, 27, -81,...... Recursive Formula an = 3 . -3n-1 an = an-1 . -3 an = an-1 + 3 an = an-1 - 9

Answer 1

$a_n=a_{n-1}\times-3^{}$

1) Considering the Sequence (3, -9, 27, -81) let's determine. which kind of Sequence is this. Examining it, it is a Geometric Sequence

$\begin{gathered} a_1=\text{ 3} \\ q=-3 \end{gathered}$

2) A Recursive formula depends on the prior term to find out the subsequent one. So we can write:

$\begin{gathered} a_n=a_1q^{n-1} \\ a_2=3(-3)^{2-1} \\ a_{2\text{ }}=3(-3)^1 \\ \end{gathered}$

3)From the explicit formula, we can derive the Recursive Formula for this Geometric Sequence:

$a_n=a_{n-1}\times-3^{}$

Note that, we can only find the subsequent term given the prior one.