Rules for Arithmetic and Geometric Sequences?

Question

Write Your Own Sequence Rule Problems
5. Think of an original arithmetic sequence where you add the same number to get from one term to the next.  

a. Write the first six elements of your sequence.

b. Identify the common difference in your sequence and use the appropriate formula to write a rule based on the sequence.

c. Use the rule to find the 50th element of your sequence.

6. Think of an original geometric sequence where you multiply each term by the same number to get to the next term.  

a. Write the first four elements of your sequence.    

b. Identify the common ratio in your sequence and use the appropriate formula to write a rule based on the sequence.    

c. Use the rule to find the sixth element of the sequence

Answer 1

(5)

Step 1:

Consider the arithmetic sequence is .

Find the common difference.

.

.

The common difference is .

Add to the third term to find the fourth term and so on.

.

.

.

The first six terms of the sequence are .

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 .

Step 3:

Find the term.

Substitute in .

.

The term is .

Solution:

(a) The first six terms of the sequence are .

(b) The common difference is ;.

(c) The term is .

Answer 2

(6)

Step 1:

Consider the geometric sequence is .

Find the common ratio .

.

The common ratio is .

Multiply the third term by to find the fourth term and so on.

.

The first four terms of the sequence are .

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 .

Step 3:

Find the sixth term.

Substitute in .

.

The sixth term is .

Solution:

(a) The first four terms of the sequence are .

(b) The common ratio is ;.

(c) The sixth term is .