1. Mid-Chapter Test Review
Module 3
Mid-Chapter Test Review

2. Describe what makes a sequence Arithmetic
Answer: Arithmetic sequences are sequences in which the terms are separated by a common difference (same number added and subtracted to each previous term). The common difference is found by subtracting the previous term.

3. Describe what makes a sequence Geometric
Answer: Geometric sequences are sequences in which the terms are separated by a common ratio (same number multiplied by each previous term). The common ratio is found by dividing the previous term.

4. Using the the sequence 9, 16, 23, 30..
Is the sequence Arithmetic or Geometric?
Answer: Arithmetic, the same term is being added each time.
What is the Common Difference?
Answer: 7
What is the recursive formula for the sequence?
Answer: f(n) = f(n-1) + 7
What is the explicit formula for the sequence (simplified)?
Answer: f(n) = 7n + 2
What is the 67th term of this sequence?
Answer: f(67) = 471

5. Given the following sequence…1 2 3 4 5 6 15
37.5
93.75
Is the sequence Arithmetic or Geometric?
Answer: Geometric, the previous term is being multiplied by the same number.
Identify the Common Ratio?
Answer: Common Ratio is 2.5
What is the Recursive formula for the sequence?
Answer: f(n) = f(n-1) x 2.5
What is the Explicit Formula for the sequence?
Answer: f(n) = 2.5 𝑛−1 x 6
What is the 13th term in the sequence?
Answer: f(13) =

6. Given the Recursive Formula f(n) = f(n-1) + 4 and f(1) = 3
What is the 6th term of the sequence?
Answer: f(6) = 23

7. Given the Graph Is the sequence Arithmetic or Geometric
What is the common difference or ratio 2

8. Johnny wants to get better grades so he decides he is going to study more. He decides that he is going to start with 15 minutes a night and increase the time by 5 minutes each night.
Is the sequence Arithmetic or Geometric?
Answer: Arithmetic
What is the Common Difference?
Answer: 5 minutes
What is the Recursive formula?
Answer: f(n) = f(n-1) +5
What is the Explicit Formula (Simplified)?
Answer: f(n) = 5(n-1) + 15
He has 20 nights to study before the big test. How much time will he spend studying on the final night?
Answer: 110 minutes or 1 hour 50 minutes