Question

Use the sequence below to complete each task. -5, 15, -45, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 12th term (22)

Answer 1

you get he common ratio by dividing a term by the previous term

so,

15/-5 = -3

common ratio = -3

Geometric seuqence has a general term of:

`a_n=ar^(n-1)`

Wher

r is common ratio

a is first term

Given,

a = -5

r = -3

We have:

`\begin{gathered} a_n=ar^(n-1) \\ a_n=-5(-3)^(n-1) \\ a_n=-5*-3^n*-3^(-1) \\ a_n=-5\cdot-3^n*-(1)/(3) \\ a_n=-(5)/(3)(3)^n \end{gathered}`

12th term is basically n = 12

So, we have:

`\begin{gathered} a_n=-(5)/(3)(3)^n \\ a_(12)=-(5)/(3)(3)^(12) \\ a_(12)=-885735_{} \end{gathered}`