Precalculus Examples

5

$5$ ,

10

$10$ ,

20

$20$

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}

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

Step 4

Substitute in the value of

n

$n$ to find the

n

$n$ th term.

a_{5} = 5 \cdot 2^{(5) - 1}

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

Step 5

Subtract

1

$1$ from

5

$5$ .

a_{5} = 5 \cdot 2^{4}

$a_{5} = 5 \cdot 2^{4}$

Step 6

Raise

2

$2$ to the power of

4

$4$ .

a_{5} = 5 \cdot 16

$a_{5} = 5 \cdot 16$

Step 7

Multiply

5

$5$ by

16

$16$ .

a_{5} = 80

$a_{5} = 80$

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