Identify the Sequence 27 , 9 , 3 , 1 , 1/3 , 1/9 , 1/27

$27$ , $9$ , $3$ , $1$ , $\frac{1}{3}$ , $\frac{1}{9}$ , $\frac{1}{27}$

Step 1

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by $\frac{1}{3}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{3}$

Step 2

This is the form of a geometric sequence.

$a_{n} = a_{1} r^{n - 1}$

Step 3

Substitute in the values of $a_{1} = 27$ and $r = \frac{1}{3}$ .

$a_{n} = 27 {(\frac{1}{3})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{3}$ .

$a_{n} = 27 \frac{1^{n - 1}}{3^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 27 \frac{1}{3^{n - 1}}$

Step 6

Combine $27$ and $\frac{1}{3^{n - 1}}$ .

$a_{n} = \frac{27}{3^{n - 1}}$

Identify the Sequence 27 , 9 , 3 , 1 , 1/3 , 1/9 , 1/27

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