Assignment: Sequences and Series
Part 1: Arithmetic, Geometric, or Neither
For problems 1-5 determine if the sequence is arithmetic, geometric, or neither. Explain your answer in 1-2 complete sentences.
1, 4, 9, 16, 25, 36,...
2. 20, 18.5, 17, 15.5, 14,...
3. 10, -9, 8, -7, 6, -5, 4, ...
4. 40, -10, 5/2, -5/8, 5/32
5. 10, 8, 5, 1, -4,...
6. For each sequence in problems 1-5 that is arithmetic, find the arithmetic sequence. Then answer the following questions.
a. Write the arithmetic sequence. What is the common difference of the sequence?
b. Write the mathematical expression that describes the arithmetic sequence.
c. Use sigma notation to describe the sum of the first ten terms of the arithmetic sequence.
d. Find the sum of the first ten terms of the arithmetic sequence.
7. For each sequence in problems 1-5 that is geometric, find the geometric sequence. Then answer the following questions.
a. Write the geometric sequence. What is the common ratio of the geometric sequence?
b. Write the mathematical expression that describes the geometric sequence.
c. Use sigma notation to describe the sum of the first ten terms of the geometric sequence.
d. Find the sum of the first ten terms of the geometric sequence.
Part 2: Create an example of a sequence
8. Write you own arithmetic or geometric sequence.
a. Write the first ten terms of your sequence.
b. Explain why your sequence is either arithmetic or geometric.
c. Write the mathematical expression that describes the arithmetic or geometric sequence.Then, use sigma notation to express the sum of the first ten terms of your sequence.
d. Write the formula for and find the sum of the first ten terms of your sequence. Identify the n, a1, and values for d or r needed to find the sum.