Rules for Arithmetic and Geometric Sequences??

Question

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,…

4. 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,…

Answer 1

(3)

Step 1:

The sequence is .

First find the common difference.

Since the common difference is equal, the sequence is a 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 .

The term of the arithmetic sequence is 39.

Answer 2

(4)

Step 1:

The sequence is .

First find the common difference.

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

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 geometric sequence.

.

The explicit formula is .

Step 3:

Find the term.

The explicit formula is .

Substitute in .

The term is

Solution:

The sequence is a geometric sequence.

The explicit formula is .

The term is