Cogito
Precalculus · Chapter 4 · Lesson 1
Arithmetic and Geometric Sequences
Adding the same, or multiplying by the same.
11 problems · about 22 minutes · TEKS P.5.B, P.5.C
What this lesson teaches
The student identifies a sequence as arithmetic or geometric and finds its nth term.
- Arithmetic sequences add a common difference; geometric ones multiply by a common ratio.
- The nth term uses n − 1 steps, because the first term takes none.
- Which kind it is decides which formula applies.
Warm Up
Straightforward practice. Get the method working first.
4 problemsa₁ = 3, d = 7. What is a₅?
Answer 31
Why 31.
2, 5, 8, 11. Common difference?
Answer 3
Why 5 − 2.
2, 5, 8, 11. What is the 5th term?
Answer 14
Why One more step.
1, 3, 9, 27. Common ratio?
Answer 3
Why 3 ÷ 1.
Build It Up
The same ideas with more to keep track of.
3 problems1, 3, 9, 27. What is the 5th term?
Answer 81
Why Multiply by 3 again.
Sort each sequence by its kind.
Answer Arithmetic: 4, 8, 12, 16, 10, 7, 4, 1 · Geometric: 4, 8, 16, 32
Why Ask whether each step adds or multiplies.
a₁ = 6, d = 5. What is a₄?
Answer 21
Why 6 + 3 × 5.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsa₁ = 2, r = 4. What is a₃?
Answer 32
Why 2 × 4 × 4.
For the nth term, how many steps are taken from the first term?
Answer 0
Why The first term itself takes none.
The Difference: 5, 9, 13, 17. What is the common difference?
Answer 4
Why 4.
The Ratio: 3, 6, 12, 24. What is the common ratio?
Answer 2
Why 2.