Algebra Examples

5

$5$ ,

10

$10$ ,

20

$20$ ; dots

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

2

$2$ gives the next term. In other words,

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

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

Geometric Sequence:

r = 2

$r = 2$

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} = 5

$a_{1} = 5$ and

r = 2

$r = 2$ .

a_{n} = 5 \cdot 2^{n - 1}

$a_{n} = 5 \cdot 2^{n - 1}$