Cogito
Integrated Math 1 · Chapter 5 · Lesson 1
Arithmetic Sequences
Adding 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 arithmetic sequences and finds any term using an explicit rule.
- An arithmetic sequence adds a constant common difference.
- aₙ = a₁ + (n − 1)d.
- Plotted against position, the terms lie on a line whose slope is d.
Warm Up
Straightforward practice. Get the method working first.
5 problemsa₁ = 5, d = 4. What is the 10th term?
Answer 41
Why 41.
Why does the formula use n − 1 rather than n?
Answer Reaching the nth term takes one fewer step than n.
Why The first term is already there.
2, 5, 8, 11. Common difference?
Answer 3
Why 5 − 2.
20, 15, 10, 5. Common difference?
Answer -5
Why 15 − 20.
a₁ = 4, d = 3. What is the 10th term?
Answer 31
Why 4 + 9 × 3.
Build It Up
The same ideas with more to keep track of.
3 problemsa₁ = 100, d = −7. What is the 5th term?
Answer 72
Why 100 − 28.
To reach the 12th term, how many steps from the first?
Answer 11
Why One fewer than the term number.
a₁ = 6, d = 5. What is the 8th term?
Answer 41
Why 6 + 35.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each sequence by whether it is arithmetic.
Answer Arithmetic: 4, 9, 14, 19, 30, 24, 18, 12 · Not arithmetic: 2, 4, 8, 16, 1, 4, 9, 16
Why Subtract consecutive terms and see whether the result repeats.
a₁ = 2, d = 6. What is the 15th term?
Answer 86
Why 2 + 84.
The Difference: 5, 12, 19, 26. What is the common difference?
Answer 7
Why 7.
The Term: a₁ = 3 and d = 4. What is the 20th term?
Answer 79
Why 79.