Arithmetic
What is the common difference of the sequence?
5, 9, 13, 17,…
4
What is the common ratio?
4, 12, 36, 108,…
3
A theater adds 4 seats to each new row. The first row has 20 seats.Which form would be most useful for finding the number of seats in the next row based on the previous row?
Recursive
Write a recursive rule for:
7, 11, 15, 19,…
f(1)=7
f(n)=f(n−1)+4
The amount of medication administered on day n is represented by M(n). M(1)=2000; M(n)=0.75M(n−1). What does M(4) represent?
A. Amount of medication administered over 4 days
B. The amount of medication administered on Day 4
C. The number of days medication was administered
D. 75% of the medication administered on Day 4
B
Find the next two terms:
24, 12, 0, −12,…
−24, −36
Find the next two terms:
2000, 1000, 500, 250,…
125, 62.5
A student saves $15 each week and starts with $40. She wants to find how much money she will have after 20 weeks without calculating the amount saved each week. Which form would be most efficient?
Explicit
Find the explicit formula:
8, 13, 18, 23,…
f(n) = 8+5(n-1)
A population of bacteria is modeled by P(n) = 500(2)^(n-1) where n represents the number of hours. What will the population be after 6 hours?
16,000
Find the 10th term:
4, 11, 18, 25,…
67
Which sequence is geometric?
A. 2,5,9,14,…
B. 1/4,1,4,16
C. 5,7,9,11,…
D. 520,420,320,220,…
B
A medication dosage decreases by multiplying the previous day's dosage by 0.75. The doctor wants to calculate the dosage for the next day using the current day's dosage. Which form would be most appropriate?
Recursive
Write a recursive rule for:
3, 9, 27, 81,…
f(1)=3
f(n)=3f(n−1)
A student is saving money for a car. The amount of money in the account after nn weeks is modeled by A(n)=50+15(n−1) where A(n) represents the amount of money saved after n weeks. How much money will the student have after 12 weeks?
215
Write an explicit formula for:
6, 10, 14, 18,…
f(n) = 6+4(n-1)
𝑓(1) = 3000, 𝑓(2) = 2250, 𝑓(3) = 1687.5, 𝑓(4) = 1265.625, 𝑓(5) = 949.21875
What is the common ratio?
0.75
A school is adding lights to a stage backdrop. The first row has 30 lights, and each new row has 6 more lights than the previous row. The teacher wants to determine the number of lights needed for the 25th row directly, without finding the number of lights in rows 2–24. Which form would be most useful?
Explicit
Write an explicit formula for:
5, -10, 20, -40,…
g(n) = 5(-2) ^ (n-1)
A school is adding 7 chairs to each new row. The number of chairs is modeled recursively: C(1)=18; C(n)=C(n−1)+7. How many chairs will be in the 9th row?
74
An arithmetic sequence has f(1)=35 and a common difference of −7. Find f(12).
-42
A geometric sequence has g(1)=48 and a common ratio of 1/2 . Find g(7).
3/4
A sequence is defined f(1)=2, f(n)=3f(n−1).
What is f(4)?
54
A sequence has f(1)=10 and f(n)=f(n−1)+6.
Which explicit formula represents the sequence?
f(n)=10+6(n-1)
Sequence A has values: 3, 8, 13, 18, 23,… Sequence B has values: 1/25, 1/5, 1, 5, 25, ... Which sequence will have the greater 9th term? By how much?
B by 15,625-43=15,582