Chapter 1 • Test



Chapter 1 • Test Form B

Name Period Date

Answer each question and show all work clearly on a separate piece of paper.

1. Here are the first three figures of a pattern.

a. (3 points) List the numbers of line segments in Figures 1–7.

b. (4 points) Write a recursive formula that generates the sequence you found in part a.

c. (3 points) How many line segments are in Figure 21?

d. (3 points) Which figure has 211 line segments?

2. Consider the sequence 0.01, 0.03, 0.09, 0.27, 0.81, ….

a. (3 points) Is the sequence arithmetic or geometric? Justify your answer.

b. (4 points) Write a recursive formula for the sequence. Use u1 to represent the starting term.

c. (3 points) What is the 9th term of the sequence?

d. (3 points) Which term of the sequence is the first to be greater than 10,000?

3. (4 points) Match a recursive formula to the graph and identify the sequence as arithmetic or geometric.

A. a0 = 75 and an = an–1 – 30 where n ≥ 1

B. a0 = 75 and an = 100 – an–1 where n ≥ 1

C. a0 = 75 and an = 0.6 ∙ an–1 where n ≥ 1

4. (3 points) A small country has a population of 2.5 million people. Each year about 4% of the previous year’s population dies or leaves the country and about 120,000 people are born or immigrate to the country. If this pattern continues, what will the population be in 5 years?

5. (4 points each) Give the recursive formula for a sequence whose graph fits the given description.

a. Nonlinear and decreasing

b. Linear and increasing

c. Nonlinear and increasing

6. (3 points each) State whether each of the following is a decrease or increase. Then state the percent that it increased of decreased.

a. From 362 m to 156 m

b. From 24 grams to 96 grams

7. (4 points each) You decide to open a savings account with $1,000 at a bank that offers a monthly interest rate of 5%.

a. Write a recursive formula.

b. Find how many months it would take to reach a balance over $1,500.

8. (3 points) State whether each statement is true or false. If the statement is false, explain why.

a. If the common difference in a sequence is 2, then to get the next term you need to add 2 from the previous term.

b. The common ratio is a number that is always divided to the previous term in order to find each subsequent term.

c. The initial term of a sequence is always u0

d. A recursive formula always uses the previous term to get the next term.

e. A discrete graph is a graph of a sequence that connects the points with a line.

f. The simple interest of a savings account is found by using sum of the principal and interest of the previous month.

g. The Sierpkinski triangle is an example of a fractal.

h. A decay sequence is a decreasing geometric sequence.

9. Suppose there are two payment options for a job. For both plans you receive $100 the first week. Under plan A, you get a 10% increase each week. Under plan B, you get a $20 raise each week.

a. (6 points) For each plan, write a recursive formula you could use to calculate your pay.

b. (4 points) Make a chart comparing the pay under each plan for the first 5 weeks.

c. (4 points) Which plan pays a higher weekly salary for the first several weeks? When does the salary from the other plan become greater?

d. (3 points) Discuss the issues you would consider when deciding which plan to take.

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