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:

$\begin{gathered} a_n=ar^{n-1} \\ a_n=-5(-3)^{n-1} \\ a_n=-5\times-3^n\times-3^{-1} \\ a_n=-5\cdot-3^n\times-\frac{1}{3} \\ a_n=-\frac{5}{3}(3)^n \end{gathered}$

12th term is basically n = 12

So, we have:

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