Cogito
Algebra 2 · Chapter 7 · Lesson 1
Arithmetic and Geometric Sequences
Adding the same, or multiplying by the same.
10 problems · about 20 minutes · F-BF.A.2, F-LE.A.2, A-SSE.B.4
What this lesson teaches
The student writes explicit and recursive rules for sequences and finds sums of series.
- Arithmetic sequences add a constant; geometric ones multiply by a constant.
- Recursive rules give the next term; explicit rules give the nth directly.
- aₙ = a₁ + (n − 1)d, and aₙ = a₁ · r^(n−1).
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Exponential Models and Compound Interest: A 25% annual rise. What is the growth factor?
Answer 1.25
Why 1.25.
Review — The Laws of Logarithms: log base 3 of 81. What is it?
Answer 4
Why 4.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSequence 6, 11, 16. What is the 10th term?
Answer 51
Why 51.
What distinguishes a geometric sequence?
Answer A constant ratio between terms.
Why A constant ratio.
Sequence 4, 7, 10. What is the 8th term?
Answer 25
Why 4 + 7 × 3.
Sequence 3, 6, 12. What is the 5th term?
Answer 48
Why Doubling.
Build It Up
The same ideas with more to keep track of.
2 problemsSequence 100, 90, 80. What is the 6th term?
Answer 50
Why Subtracting 10.
Sequence 1, 2, 4, 8. Arithmetic or geometric?
Answer Geometric.
Why A constant ratio.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Tenth Term: Sequence 2, 5, 8, 11. What is the 10th term?
Answer 29
Why 29.
The Geometric One: Sequence 2, 6, 18, 54. What is the 5th term?
Answer 162
Why 162.