Algebra Examples

2

$2$ ,

6

$6$ ,

18

$18$ ,

54

$54$

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} = 2

$a_{1} = 2$ and

r = 3

$r = 3$ .

a_{n} = 2 \cdot 3^{n - 1}

$a_{n} = 2 \cdot 3^{n - 1}$

2, 6, 18, 54

$2, 6, 18, 54$

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