Cogito
Integrated Math 1 · Chapter 5 · Lesson 2
Geometric Sequences
Multiplying the same amount each time.
12 problems · about 20 minutes · F-BF.A.2, F-LE.A.2
What this lesson teaches
The student identifies geometric sequences and finds any term using an explicit rule.
- A geometric sequence multiplies by a constant common ratio.
- aₙ = a₁ · r^(n−1).
- Arithmetic sequences are linear; geometric sequences are exponential.
Warm Up
Straightforward practice. Get the method working first.
5 problemsa₁ = 4, r = 3. What is the 4th term?
Answer 108
Why 108.
A geometric sequence corresponds to which kind of function?
Answer An exponential function.
Why Exponential, with the ratio as the base.
2, 6, 18, 54. Common ratio?
Answer 3
Why 6 ÷ 2.
80, 40, 20, 10. Common ratio?
Answer 0.5
Why 40 ÷ 80.
a₁ = 5, r = 2. What is the 4th term?
Answer 40
Why 5 × 8.
Build It Up
The same ideas with more to keep track of.
3 problemsa₁ = 1, r = 3. What is the 5th term?
Answer 81
Why 3 to the fourth.
2, −6, 18, −54. Common ratio?
Answer -3
Why −6 ÷ 2.
a₁ = 100, r = 0.5. What is the 4th term?
Answer 12.5
Why Halve three times.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each sequence by its type.
Answer Arithmetic: 3, 8, 13, 18, 50, 45, 40, 35 · Geometric: 5, 15, 45, 135, 64, 32, 16, 8
Why Check subtraction first, then division.
a₁ = 2, r = 4. What is the 4th term?
Answer 128
Why 2 × 64.
The Ratio: 4, 12, 36, 108. What is the common ratio?
Answer 3
Why 3.
The Term: a₁ = 3 and r = 2. What is the 6th term?
Answer 96
Why 96.