Algebra Examples

0.2

$0.2$ ,

0.1

$0.1$ ,

0.05

$0.05$ ,

0.025

$0.025$

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

$0.5$ gives the next term. In other words,

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

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

Geometric Sequence:

r = 0.5

$r = 0.5$

Step 2

This is the form of a geometric sequence.

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

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

Step 3

Substitute in the values of

a_{1} = 0.2

$a_{1} = 0.2$ and

r = 0.5

$r = 0.5$ .

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

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

Step 4

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

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

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

Step 5

Subtract

1

$1$ from

5

$5$ .

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

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

Step 6

Raise

0.5

$0.5$ to the power of

4

$4$ .

a_{5} = 0.2 \cdot 0.0625

$a_{5} = 0.2 \cdot 0.0625$

Step 7

Multiply

0.2

$0.2$ by

0.0625

$0.0625$ .

a_{5} = 0.0125

$a_{5} = 0.0125$