Sequence Type
3, 7, 11, 15, 19
Arithmetic
Write an explicit and recursive equation for the sequence: 5, 8, 11, 14
E: f(x) = 5 + 3(n − 1)
R: f(x)=f(x-1)+3; f(1)=5
Find the missing arithmetic terms: 12, ___, ___, 27
17, 22
Given f(x)=3x+5, find f(4).
A theater has 12 seats in the first row. Each row after that has 4 more seats than the previous row. How many seats are in the 8th row?
2, 6, 18, 54, 162
Geometric
Write the recursive and explicit equation for the sequence: 4, 12, 36, 108
R: f(x)=f(x-1) x 3; f(1)=4
E: f(x)=4(3)^(x-1)
Find the missing geometric terms: 5, ___, ___, 135
15, 45
Given f(x)=2x2−3, find f(−3).
15
A bacteria population starts at 200 and doubles every hour. How many bacteria will there be after 5 hours?
6400 bacteria
12, 17, 22, 27, 32
Arithmetic
The recursive rule is a₁ = 7, aₙ = aₙ₋₁ + 5. Write the explicit equation.
aₙ = 7 + 5(n − 1) OR f(x)=7 + 5(n − 1)
Find the missing geometric terms:
48, ___, ___, ___, 3
24, 12, 6
Given f(x)=5(2)^x, find f(4).
80
A car worth $28,000 depreciates by 12% each year. What will it be worth after 5 years?
≈ $14,755.73
81, 27, 9, 3, 1
Geometric
The explicit rule is aₙ = 3(2)ⁿ⁻¹. Write the recursive equation.
a₁ = 3
aₙ = 2aₙ₋₁
OR
f(x)=f(x-1) x 2; f(1)=3
Find the missing arithmetic terms:
7, ___, ___, ___, ___, 39
13.4, 19.8, 26.2, 32.6
Given f(x)=x^2-4x+7, find when f(x)=19.
-2
A town has 15,000 people and grows by 2.5% each year. Write an explicit equation and determine the population after 8 years.
P(n)=15000(1.025)n
≈ 18,275 people
4, 9, 16, 25, 36
Neither
Write the recursive for this function: aₙ = 6(1.5)ⁿ⁻¹
a₁ = 6
aₙ = 1.5aₙ₋₁
Find the missing geometric temrs:
4096, ___, ___, ___, ___, 4
1024, 256, 64, 16
Given f(x)=2x^2-5x+6, find f(−3)+f(2).
43
A video game's number of active players decreases by 8% each month. The game currently has 12,500 active players.
Part A: Write an explicit function.
Part B: Predict the number of players after 7 months.
Part C: Explain why this situation represents a geometric sequence.
P(n)=12500(0.92)n
After 7 months: ≈ 7,081 players
Common ratio: 0.92, because the population retains 92% each month.