Arithmetic, geometric, or neither?
Classify the sequence as arithmetic, geometric, or neither. Give the common difference or common ratio if one exists.
11, 17, 23, 29, 35, ...
Answer: Arithmetic; common difference = 6
An arithmetic sequence has a first term of 14 and a fourth term of 35.
Find the second and third terms.
Answer: 21, 28
Write an explicit equation and a recursive equation for the sequence.
8, 13, 18, 23, 28, ...
Answer:
Explicit: f(n) = 5n + 3
Recursive: f(1) = 8; f(n) = f(n - 1) + 5
Maya has $40 in her savings account. She deposits $15 every week.
Write an explicit equation representing the amount of money in her account after n weeks, where week 1 is the first week.
Answer:
f(n) = 40 + 15(n - 1)
The table represents a sequence.
n: 1 | 2 | 3 | 4 | 5
f(n): 6 | 11 | 16 | 21 | 26
What type of sequence is represented, and what is the common difference?
Answer: Arithmetic; common difference = 5
Classify the sequence as arithmetic, geometric, or neither. Give the common difference or common ratio if one exists.
96, 48, 24, 12, 6, ...
Answer: Geometric; common ratio = 1/2
A geometric sequence has a first term of 5 and a sixth term of 1,215.
Find the four missing terms.
Answer: 15, 45, 135, 405
Write an explicit equation and a recursive equation for the sequence.
81, 27, 9, 3, 1, ...
Answer:
Explicit: f(n) = 81(1/3)^(n - 1)
Recursive: f(1) = 81; f(n) = (1/3)f(n - 1)
A theater has 18 seats in the first row. Each successive row has 4 more seats than the previous row.
How many seats are in the 15th row?
Answer: 74 seats
The table represents a sequence.
n: 1 | 2 | 3 | 4
f(n): 3 | 12 | 48 | 192
Write an explicit equation for the sequence.
Answer:
f(n) = 3(4)^(n - 1)
Classify the sequence as arithmetic, geometric, or neither. Explain how you know.
5, -10, 20, -40, 80, -160, ...
Answer: Geometric; common ratio = -2
An arithmetic sequence has a first term of -17 and a seventh term of 37.
Find all five missing terms.
Answer: -8, 1, 10, 19, 28
An arithmetic sequence has a third term of 17 and an eighth term of 52.
Write an explicit equation and a recursive equation.
Answer:
Common difference = 7
Explicit: f(n) = 7n - 4
Recursive: f(1) = 3; f(n) = f(n - 1) + 7
A student deposits $25 during the first week. Each week, she deposits 20% more than she deposited the previous week.
Write an explicit equation and a recursive equation representing the amount deposited during week n.
Answer:
Explicit: f(n) = 25(1.2)^(n - 1)
Recursive: f(1) = 25; f(n) = 1.2f(n - 1)
A graph contains the points:
(1, 7), (2, 12), (3, 17), (4, 22), (5, 27)
What type of sequence is represented?
What is the common difference?
Write an explicit equation.
What is the 20th term?
Answer:
Arithmetic
Common difference = 5
Explicit equation: f(n) = 5n + 2
20th term = 102
Classify the sequence as arithmetic, geometric, or neither. Explain how you know.
7, 14, 28, 56, 112, 225, ...
Answer: Neither
A geometric sequence has a first term of 3 and a seventh term of 2,187.
Find all five missing terms.
Answer: 9, 27, 81, 243, 729
A geometric sequence has a second term of 12 and a fifth term of 324.
Write an explicit equation and a recursive equation.
Answer:
Common ratio = 3
First term = 4
Explicit: f(n) = 4(3)^(n - 1)
Recursive: f(1) = 4; f(n) = 3f(n - 1)
A company's starting salary is $52,000. Employees receive a guaranteed 3% raise each year.
Write an explicit equation representing the salary during year n, where year 1 is $52,000.
Then find the salary during the 10th year.
Answer:
f(n) = 52,000(1.03)^(n - 1)
10th year ≈ $67,828.86
A sequence is represented by the explicit equation:
f(n) = 6(2)^(n - 1)
Complete the table.
n: 1 | 2 | 3 | 4 | 5 | 6
f(n): 6 | ___ | 24 | ___ | ___ | ___
Then state whether the sequence is arithmetic or geometric.
Answer:
6 | 12 | 24 | 48 | 96 | 192
Geometric; common ratio = 2
Classify the sequence as arithmetic, geometric, or neither. Explain how you know.
-243, 81, -27, 9, -3, 1, ...
Answer: Geometric; common ratio = -1/3
A geometric sequence has a first term of 5 and a sixth term of 15,625.
Find all four missing terms.
Answer: 25, 125, 625, 3,125
A geometric sequence has a fourth term of -54 and a seventh term of 1,458.
Write an explicit equation and a recursive equation.
Answer:
Common ratio = -3
First term = 2
Explicit: f(n) = 2(-3)^(n - 1)
Recursive: f(1) = 2; f(n) = -3f(n - 1)
A video has 800 views on its first day. Each day, the number of views is 1.5 times the number from the previous day.
Answer:
f(n) = 800(1.5)^(n - 1)
The first day is Day 15.
The table represents a sequence.
n: 1 | 2 | 3 | 4 | 5
f(n): 160 | 80 | 40 | 20 | 10
Without simply continuing the pattern one term at a time:
Answer: