Question

Use the sequence below to complete each task. 972, 324, 108, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 6th term (ac)

Answer 1

(a),

The common ratio between the terms is

$\frac{972}{324}=\frac{324}{108}=3$

(b).

The common ratio found in (a) tells us that every next number is found by dividing the previous number by 3; therefore, the equation for a_n the nth term will be

$a_n=\frac{972}{3^n}$

(c).

The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us

$a_6=\frac{972}{3^6}=\frac{4}{3}$