Question

Write the first five terms of the sequence where the first term is $7$ and the common ratio is $r=-3$.

Short answer

First five terms are$7,-21,63,-189,567$.

Step-by-step solution

Step 1. Write the first five terms of the sequence.

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

$\begin{array}{rcl}a& =& 7\\ r& =& -3\end{array}$

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

$\begin{array}{rcl}{a}_2& =& 7{\left(-3\right)}^{2-1}\\ & =& -21\\ a_3& =& 7{\left(-3\right)}^{3-1}\\ & =& 63\\ a_4& =& 7{\left(-3\right)}^{4-1}\\ & =& -189\\ a_5& =& 7{\left(-3\right)}^{5-1}\\ & =& 567\\ & & \end{array}$

So, the first five terms are

$7,-21,63,-189,567$