Question

Please answer part 2 through part 5 so I can have a full understanding

Answer 1

The formula of geometeric sequence is given as

`\begin{gathered} a_n=ar^(n-1) \\ where\text{ n = nth term} \\ r=common\text{ ratio} \\ a=first\text{ term = -1} \end{gathered}`

From the sequence given, the 3rd term is -36. So we have

`\begin{gathered} a_3=-1(r)^(3-1) \\ -36=-1r^2 \\ 36=r^2 \\ r=√(36)=6 \end{gathered}`

So we got the common ratio as 6. Let's see if it works for the fourth term 216, we have

`\begin{gathered} a_4=-1(6^(4-1)) \\ =-1(6^3) \\ =-1*216 \\ =-216 \end{gathered}`

We got -216 and not 216. So that means the common ratio r = -1.

Note that 6 square and (-6) square gives 36

Let's check

`\begin{gathered} a_4=-1(-6)^3 \\ =-1(-216) \\ =216 \end{gathered}`

Hence r = -6

So, the second term is

`\begin{gathered} a_2=a* r \\ =-1*-6 \\ =6 \end{gathered}`

The fifth term becomes

`\begin{gathered} a_5=-1(-6)^(5-1) \\ =-1(-6)^4 \\ =-1*1,296 \\ =-1,296 \end{gathered}`

Hence the geometric sequence is

-1, 6, -36, 216, -1296

The growth factor is the common ratio which is -6