12.1.A.1Multiple Choice
Which statement about a sequence is correct?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions 1–10 cover 2.1.A; questions 11–20 cover 2.1.B (question 20 uses both). In every problem, the first term of a sequence is the term at n = 0.
Which statement about a sequence is correct?
Select A, B, C, or D to check your answer.
A sequence is defined by an = 4n − 3 for whole numbers n. (a) Find a0, a3, and a10. (b) Which term in the list is a3?
The graph shows the first five terms of a sequence an, for n = 0, 1, 2, 3, 4. Which statement is correct?
Select A, B, C, or D to check your answer.
A channel has 1,200 subscribers at the start (day 0) and gains 30 subscribers each day. Let sn be the number of subscribers at the end of day n. (a) Identify the input and the output of s. (b) Evaluate s7 and explain what it means. (c) Describe the graph of s.
Each list shows the first five terms of a sequence. Which sequence is arithmetic?
Select A, B, C, or D to check your answer.
The table gives the height hn of a plant, in centimeters, n weeks after it was measured at 6 cm. Show that the sequence is arithmetic and state the common difference. What does the common difference mean in this context?
| n (weeks) | 0 | 1 | 2 | 3 | 4 |
| hn (cm) | 6 | 9.5 | 13 | 16.5 | 20 |
In an arithmetic sequence, a2 = 11 and a3 = 7. What is a4?
Select A, B, C, or D to check your answer.
An arithmetic sequence has initial value a0 = 5 and common difference d = 4. Which expression gives the general term an?
Select A, B, C, or D to check your answer.
An arithmetic sequence has a3 = 20 and common difference d = −3. Which expression gives an?
Select A, B, C, or D to check your answer.
Two terms of an arithmetic sequence are a2 = 13 and a7 = 33. (a) Find the common difference. (b) Write an in the form a0 + dn. (c) Find a15.
Each list shows the first five terms of a sequence. Which sequence is geometric?
Select A, B, C, or D to check your answer.
The table gives the first five terms of a sequence. Show that it is geometric, state the common ratio, and describe the proportional change from one term to the next.
| n | 0 | 1 | 2 | 3 | 4 |
| gn | 8 | 12 | 18 | 27 | 40.5 |
In a sequence of positive terms, each term is 80% of the term before it. What is the common ratio, and is the sequence increasing or decreasing?
Select A, B, C, or D to check your answer.
A geometric sequence has initial value g0 = 6 and common ratio r = 3. Which expression gives the general term gn?
Select A, B, C, or D to check your answer.
A geometric sequence has g2 = 20 and common ratio r = 0.5. What is g4?
Select A, B, C, or D to check your answer.
An increasing geometric sequence has g3 = 24 and g6 = 192. (a) Find the common ratio. (b) Write gn in the form g0rn. (c) Find g8.
A phone is worth $800 when new and loses 15% of its value each year. Assume the value drops once at the end of each whole year, and let gn be its value after n years. (a) Find the common ratio. (b) Write gn. (c) Find g3 to the nearest cent.
The table gives an arithmetic sequence an and a geometric sequence gn. Which statement correctly compares how the two sequences increase?
| n | 0 | 1 | 2 | 3 | 4 |
| an | 4 | 7 | 10 | 13 | 16 |
| gn | 4 | 6 | 9 | 13.5 | 20.25 |
Select A, B, C, or D to check your answer.
Plan A: a savings account starts with $200 and adds $20 each month. Plan B: a savings account starts with $200 and grows by 10% each month. (a) Write a general term for each plan. (b) Compare the increases in the first three months for each plan. (c) Which plan has the larger balance after 12 months, and by how much (to the nearest dollar)?
Sequence A: 3, 7, 11, 15, … Sequence G: 3, 6, 12, 24, … (the first term of each is the term at n = 0). (a) Classify each sequence as arithmetic or geometric and give its common difference or common ratio. (b) Write the general term of each. (c) Find the smallest n for which gn > an, and explain why G stays ahead after that.