Category 1: Arithmetic Sequences
What is the common difference in the sequence 3, 7, 11, 15?
Answer: 4
What does f(x) typically represent?
A function of x
Find the 5th term of the sequence: 2, 5, 8, ...
Answer: 11
Write a function to represent the cost of 5 apples at $0.50 each
Answer: f(x) = 0.50x
where x = number of apples
so f(5) = 2.50
Identify the next term in the sequence: 4, 8, 12, ...
Answer: 16
Write the formula for the nth term of the sequence: 5, 10, 15, ...
a(n) = 5n
If f(x) = 3x + 2, what is f(4)
Answer: 14
What is the 10th term of the sequence: 1, 4, 7, ...
Answer: 28
If a car's value decreases by $1,000 each year, model this situation with a function.
Answer: f(x) = initial value - 1000x
What pattern do you notice in the sequence: 10, 20, 30, ...
Answer: The sequence increases by 10 each time.
How do you determine the first term and common difference of a sequence?
Answer: The first term is the initial value, and the common difference is the amount added to each term.
If g(x) = 2x - 5, what is g(3)?
Answer: 1
Find the 12th term of the sequence: -2, 1, 4, ...
Answer: 34
A savings account earns $50 monthly. Write a function for total savings after x months.
Answer: f(x) = 50x
What is the next term in the sequence: 1, 3, 6, 10, ...?
Answer: 15
Describe how an arithmetic sequence differs from a geometric sequence
Answer: An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio.
If f(x) = x² + 1, what is f(5)?
Determine the 15th term of the sequence: 7, 12, 17, ...
Answer: 82
Model the total distance traveled if a bike moves 10 miles every hour for x hours.
Answer: d(x) = 10x
Identify the pattern in the sequence: 100, 90, 80, ...
Answer: The sequence decreases by 10 each time.
Create an arithmetic sequence with a first term of 10 and a common difference of 4.
Answer: 10, 14, 18, 22, ...
What is the inverse of the function f(x) = 2x + 6?
Answer: f⁻¹(x) = (x - 6)/2
How do you find the value of n if the nth term is 50 in the sequence 4, 8, 12, ...?
Answer: n = 13
Write a function to represent the population growth of a town increasing by 200 residents each year.
Answer: P(x) = initial population + 200x
Create a sequence based on the formula: 5n - 1 for n = 1, 2, 3, ...
Answer: 4, 9, 14, 19, ...