Find the 6th Term 7640 , 764 , 76.4 , 7.64

$7640$ , $764$ , $76.4$ , $7.64$

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 $\frac{1}{10}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{10}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 7640$ and $r = \frac{1}{10}$ .

$a_{n} = 7640 {(\frac{1}{10})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{10}$ .

$a_{n} = 7640 \frac{1^{n - 1}}{10^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 7640 \frac{1}{10^{n - 1}}$

Step 6

Combine $7640$ and $\frac{1}{10^{n - 1}}$ .

$a_{n} = \frac{7640}{10^{n - 1}}$

Step 7

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

$a_{6} = \frac{7640}{10^{(6) - 1}}$

Step 8

Simplify the denominator.

Subtract $1$ from $6$ .

$a_{6} = \frac{7640}{10^{5}}$

Raise $10$ to the power of $5$ .

$a_{6} = \frac{7640}{100000}$

Step 9

Cancel the common factor of $7640$ and $100000$ .

Factor $40$ out of $7640$ .

$a_{6} = \frac{40 (191)}{100000}$

Cancel the common factors.

Factor $40$ out of $100000$ .

$a_{6} = \frac{40 \cdot 191}{40 \cdot 2500}$

Cancel the common factor.

$a_{6} = \frac{40 \cdot 191}{40 \cdot 2500}$

Rewrite the expression.

$a_{6} = \frac{191}{2500}$

Find the 6th Term 7640 , 764 , 76.4 , 7.64

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