Find the Next Term 1/3 , 2 , 12 , 72

$\frac{1}{3}$ , $2$ , $12$ , $72$

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 $6$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 6$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = \frac{1}{3}$ and $r = 6$ .

$a_{n} = \frac{1}{3} \cdot 6^{n - 1}$

Step 4

Combine $\frac{1}{3}$ and $6^{n - 1}$ .

$a_{n} = \frac{6^{n - 1}}{3}$

Step 5

Substitute in the value of $n$ to find the $n$ th term.

$a_{5} = \frac{6^{(5) - 1}}{3}$

Step 6

Simplify the numerator.

Subtract $1$ from $5$ .

$a_{5} = \frac{6^{4}}{3}$

Raise $6$ to the power of $4$ .

$a_{5} = \frac{1296}{3}$

Step 7

Divide $1296$ by $3$ .

$a_{5} = 432$

Find the Next Term 1/3 , 2 , 12 , 72

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