Algebra Examples

6

$6$ ,

18

$18$ ,

54

$54$ ,

162

$162$ ,

486

$486$

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

3

$3$ gives the next term. In other words,

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

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

Geometric Sequence:

r = 3

$r = 3$

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} = 6

$a_{1} = 6$ and

r = 3

$r = 3$ .

a_{n} = 6 \cdot 3^{n - 1}

$a_{n} = 6 \cdot 3^{n - 1}$