Question

Identify the type of sequence. Write the explicit formula, then use the formula to find the 13th term. 6, 18, 54, 162... 0:00 D A Geometric, an=6(3)n-1, a 13=9,565,938 B Arithmetic, an=6+3(n-1), a 13=42

Answer 1

The sequence is:

6, 18, 54, 162.......

By proper observation of the sequence above, you would notice that there is a common ratio of 3.

That is, r = 18 / 6 = 54 / 18 = 162 / 54 = 3

Common ratio, r = 3

The first value in the sequnce is a = 6

Since the sequnce has a common ratio, it is a geometric sequence.

The formula for the nth term of a Geometric sequence is:

$a_n=ar^{n-1}$

To get the 13th term of the sequnce, n = 13

$\begin{gathered} a_{13}=(6)(3)^{13-1} \\ a_{13}=6(3)^{12} \\ a_{13}=\text{ }6\times531441 \\ a_{13}=\text{ }3188646 \end{gathered}$