Find the 6th Term 12 , 2 , 1/3 , 1/18

$12$ , $2$ , $\frac{1}{3}$ , $\frac{1}{18}$

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

Geometric Sequence: $r = \frac{1}{6}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 12$ and $r = \frac{1}{6}$ .

$a_{n} = 12 {(\frac{1}{6})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{6}$ .

$a_{n} = 12 \frac{1^{n - 1}}{6^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 12 \frac{1}{6^{n - 1}}$

Step 6

Combine $12$ and $\frac{1}{6^{n - 1}}$ .

$a_{n} = \frac{12}{6^{n - 1}}$

Step 7

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

$a_{6} = \frac{12}{6^{(6) - 1}}$

Step 8

Simplify the denominator.

Subtract $1$ from $6$ .

$a_{6} = \frac{12}{6^{5}}$

Raise $6$ to the power of $5$ .

$a_{6} = \frac{12}{7776}$

Step 9

Cancel the common factor of $12$ and $7776$ .

Factor $12$ out of $12$ .

$a_{6} = \frac{12 (1)}{7776}$

Cancel the common factors.

Factor $12$ out of $7776$ .

$a_{6} = \frac{12 \cdot 1}{12 \cdot 648}$

Cancel the common factor.

$a_{6} = \frac{12 \cdot 1}{12 \cdot 648}$

Rewrite the expression.

$a_{6} = \frac{1}{648}$

Find the 6th Term 12 , 2 , 1/3 , 1/18

Related Questions

Support LCMGCF.com by disabling your adblocker.