Precalculus Examples

7

$7$ ,

21

$21$ ,

63

$63$

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} = 7

$a_{1} = 7$ and

r = 3

$r = 3$ .

a_{n} = 7 \cdot 3^{n - 1}

$a_{n} = 7 \cdot 3^{n - 1}$

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