### Home > CCA > Chapter 6 > Lesson 6.2.5 > Problem6-112

6-112.

For the recursively defined sequence:
$a_1=5$
$a_n=−2·a_{n−1}$

1. List the first five terms of the sequence.

Start by finding the second term in the sequence. Don't forget that the first term of the sequence is $5!$

$a_{2} = −2 · a_{2−1}$
$a_{2} = −2 · a_{1}$
$a_{2} = −2 · 5$
$a_{2} = −10$

Repeat the above process for the next three terms of the sequence.

2. Write an explicit equation for the sequence.

What is the zeroth term?

What is the multiplier?

$a_{n}=-\frac{5}{2}(-2)^n$