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 (as)

Answer 1

The ratio of a sequence can be found by dividing a term by its previous, we have:

$r\text{ = }\frac{324}{972}=\frac{1}{3}$

If this is a geometric sequence the ratio should be the same for all the terms, so let's test with the other pair of terms:

$r=\frac{108}{324}=\frac{1}{3}$

Since the ratio is the same it is a geometric sequence. We can then write the expression to represent it as shown below:

$a_n=972\cdot\frac{1}{3}^{n-1}$

To find the 6th term we need to use n as equal to 6 in the expression above, we have:

$\begin{gathered} a_6=972\cdot\frac{1}{3}^{6-1} \\ a_6=972\cdot\frac{1}{729}=1\frac{1}{3} \end{gathered}$

The sixth term is 1 1/3 or 1.33333...