Write Rules for Arithmetic and Geometric Sequences \ \ 3. Identify the common difference OR common ratio, depending on whether the sequence below is arithmetic or geometric. Then use the appropriate formula to write a rule for the sequence. Finally, use the rule to find the tenth term in the sequence. \ \ –15, –9, –3, 3, 9,…

(3)

Step 1:

The series is .

First find the common difference.

Since the common difference is equal, the series is arithmetic sequence.

Step 2:

Find the explicit formula for term.

Formula for term of arithmetic sequence is .

Substitute  and  in term of arithmetic sequence.

.

The explicit formula is .

Step 3:

Find the term:

The explicit formula is .

Substitute in .

.

The term is 39.

Solution:

The series is arithmetic sequence.

The explicit formula is .

Identify the common difference OR common ratio, depending on whether the sequence below is arithmetic or geometric. Then use the appropriate formula to write a rule for the sequence. Finally, use the rule to find the ninth term in the sequence. \ \ –4, 12, –36, 108, –324,…

(3)

Step 1:

The sequence is .

First find the common difference.

Since the common difference is not equal, the sequence is not a arithmetic sequence.

First find the common ratio.

Since the common ratio is equal, the sequence is a geometric sequence.

Step 2:

Find the explicit formula for term.

Formula for term of geometric sequence is .

Substitute  and  in term of arithmetic sequence.

.

The explicit formula is .

Step 3:

Find the term.

The explicit formula is .

Substitute in .

\ \

The term is

Solution:

The series is arithmetic sequence.

The explicit formula is .