Question

How do you write the next three terms of the geometric sequence `-2, -12, -72, -432,...` and graph the sequence?

Answer 1

The next three terms are:`" "-2592," "-15552," "-93312`

Explanation:

To determine the next three terms we have to study the given
`" "`
terms in this sequence and how it is calculated .
`" "`
`" "`
`a_0=-2`
`" "`
`a_1=-2 xx color(blue)(6^1)=-12`
`" "`
`a_2=-2 xx color(blue)(6^2)= -72`
`" "`
Therefore, `" "a_n=-2xxcolor(blue)(6^n)`
`" "`
What is `a_4=?, a_5" =?",a_6=?`
.`" "`
`a_4=-2xx6^4=-2xx1296=-2592`
`" "`
`a_5=-2xx6^5=-2xx7776=-15552`
`" "`
`a_6=-2xx6^6=-2xx46656=-93,312`
`""`
The geometric series is:
`" "`
`-2," "-12," "-72," "-432," "-2592," "-15552," "-93312`