Algebra Homework help

Question

Give an example of an arithmetic sequence that is found in the real world. Find the common difference and write a recursive and iterative rule for the sequence. Use one of the rules to find another term of the sequence.

Then give an example of a geometric sequence that is found in the real world. Find the common ratio and write a recursive and iterative rule for the sequence. Use a rule to find any term.

Then clearly explain why each example is either an arithemetic or geometric sequence.

Answer 1

(1)

Step 1:

The sequence is .

First find the common difference.

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

Find the explicit formula for term.

Formula for term of arithmetic sequence is .

Substitute  and  in term of arithmetic sequence.

.

Find the term.

The explicit formula is .

Substitute in .

.

The term is 39.

Solution:

The term of the arithmetic sequence is 39.

Answer 2

(2)

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 .

Find the term.

The explicit formula is .

Substitute in .

The term is

Solution:

The term is