Question

Write the first five terms of the sequence where the first term is $6$and the common ratio is $r=-4$.

Short answer

The first five terms are$6,-24,96,-384,1536$

Step-by-step solution

Step 1. Given information

The first term is $6$and the common ratio is $r=-4$.

Step 2. Write the first five terms of the sequence.

Let$a,r$denote the first term and the common ratio.

localid="1645292195496" $\begin{array}{rcl}a& =& 6\\ r& =& -4\end{array}$

localid="1645292202355" $\begin{array}{rcl}{a}_n& =& a{r}^{n-1}\\ a_2& =& 6{(-4)}^{2-1}=-24\\ a_3& =& 6{(-4)}^{3-1}=96\\ a_4& =& 6{(-4)}^{4-1}=-384\\ a_5& =& 6{(-4)}^{5-1}=1536\end{array}$