Algebra Examples

$0.2$ , $0.1$ , $0.05$ , $0.025$

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 $0.5$ gives the next term. In other words, $a_{n} = a_{1} r^{n - 1}$ .

Geometric Sequence: $r = 0.5$

Step 2

This is the form of a geometric sequence.

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

Step 3

Substitute in the values of $a_{1} = 0.2$ and $r = 0.5$ .

$a_{n} = 0.2 \cdot {0.5}^{n - 1}$

Step 4

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

$a_{5} = 0.2 \cdot {0.5}^{(5) - 1}$

Step 5

Subtract $1$ from $5$ .

$a_{5} = 0.2 \cdot {0.5}^{4}$

Step 6

Raise $0.5$ to the power of $4$ .

$a_{5} = 0.2 \cdot 0.0625$

Step 7

Multiply $0.2$ by $0.0625$ .

$a_{5} = 0.0125$