Find the Next Term 100 , 20 , 4 , 4/5

$100$ , $20$ , $4$ , $\frac{4}{5}$

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 $\frac{1}{5}$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = \frac{1}{5}$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 100$ and $r = \frac{1}{5}$ .

$a_{n} = 100 {(\frac{1}{5})}^{n - 1}$

Step 4

Apply the product rule to $\frac{1}{5}$ .

$a_{n} = 100 \frac{1^{n - 1}}{5^{n - 1}}$

Step 5

One to any power is one.

$a_{n} = 100 \frac{1}{5^{n - 1}}$

Step 6

Combine $100$ and $\frac{1}{5^{n - 1}}$ .

$a_{n} = \frac{100}{5^{n - 1}}$

Step 7

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

$a_{5} = \frac{100}{5^{(5) - 1}}$

Step 8

Simplify the denominator.

Subtract $1$ from $5$ .

$a_{5} = \frac{100}{5^{4}}$

Raise $5$ to the power of $4$ .

$a_{5} = \frac{100}{625}$

Step 9

Cancel the common factor of $100$ and $625$ .

Factor $25$ out of $100$ .

$a_{5} = \frac{25 (4)}{625}$

Cancel the common factors.

Factor $25$ out of $625$ .

$a_{5} = \frac{25 \cdot 4}{25 \cdot 25}$

Cancel the common factor.

$a_{5} = \frac{25 \cdot 4}{25 \cdot 25}$

Rewrite the expression.

$a_{5} = \frac{4}{25}$

Find the Next Term 100 , 20 , 4 , 4/5

Related Questions

Support LCMGCF.com by disabling your adblocker.