4.7 Arithmetic Sequences, Part 1: Recursive Equations
Act 1: Definition of a sequence
a. Draw figure 5 and figure 6 if the pattern was to continue.
Figure 5
b. How many dots are in each figure?
Figure 6
c. Describe.
Act 2: Copy the recursive equation from the flipchart. _________________________________
a. Copy each of the sets of numbers from the flipchart: If you do not have an arithmetic sequence,
then explain why not. If you do have an arithmetic sequence, then write the recursive equation for it.
i)
ii)
iii)
Copy the sequences from the flipchart. Write the next three terms and write the recursive equation.
Sequence
Next three terms
Recursive Equation
b. ____, ____, ____, …
c. ____, ____, ____, ____, ….
d. ____, ____, ____, …
e. Copy the recursive equation from the flipchart and write the first 5 terms in the sequence.
f. Copy the sets of numbers from the flipchart. Are either of these arithmetic sequences?
Show work and explain.
i. _____, _____, _____,…
ii. _____, _____, _____,…
Act 3: More work with Recursive Equations
a. Copy the sequence from the flipchart : ____, ____, ____, ____, …
a3 = 2. Explain why.
b. a4= _____ a5= _____ a6= _____
c. _________
Act 4: Copy the table from the flipchart and use the sequence described in the table to answer a-d.
a. Is this sequence arithmetic? Justify your answer.
b. What is a6? _________
c. Write the recursive equation. _________________________________________
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d. Copy the equation from the flipchart and create a table of values for it. ________________
e. For the sequence represented in your table in part d, what is u8? _________
f. CHALLENGE: How would you find u35?
Act 5: Practice/Homework. For questions #1 – 4:
 Determine whether or not the sequence is arithmetic. Justify your answer.
 If it is arithmetic, write a recursive equation .
 Find a7.
Sequence
Is it Arithmetic? Justify!
Recursive Equation
1. 256, 64, 16, 4, . . .
a7
2. 14, 6, -2, -10, . . .
3. 1.2, 2.4, 3.6, 4.8, . . .
4. 4, 40, 400, 4000, . .
.
For questions #5-7, write the first six terms in the sequence. Explain what the sixth term means in the
context of the situation.
5. You have borrowed$450 from your grandmother. Each week you pay her back $30.
a1
a2
a3
a4
a5
a6
Explanation of the sixth term in the context of this situation.
6. A baby anteater weighs 2 lbs. the first month, and gains 3 lbs. every month.
a1
a2
a3
a4
a5
a6
Explanation of the sixth term in the context of this situation.
7. You long-jump 8 meters the first track meet, then you improve by 1 cm each event.
a1
a2
a3
a4
a5
a6
Explanation of the sixth term in the context of this situation.
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