Chapter 7.8, Problem 31PPE

To determine

To Write: Write the explicit and recursive formula for the given geometric sequence.

Answer to Problem 31PPE

The recursive formula is $a_n=a_{n-1}.\left(-4\right);a_1=2$

Explanation of Solution

Given information : The given sequence is $2,-8,32,-64,\dots$

Here the geometric sequence is $2,-8,32,-64,\dots$

Here the first term is $a_1=2$ and common ratio = $r=\frac{-8}{2}=-4$

The recursive formula is

  $a_n=a_{n-1}.r;a_1=2$

Now, substituting the value of r

  $a_n=a_{n-1}.\left(-4\right);a_1=2$