Sweet BBQ
Find the missing terms of the arithmetic sequence. Write the explicit and recursive equations.
5, __, __, __, 65
d=15
5, 20, 35, 50, 65
y=15(x-1)+5 OR y=15x-10
Next=Previous+15
f(n)=f(n-1)+15
f(2)=20
Find the missing terms of the geometric sequence. Write the explicit and recursive equations.
2, __, __, 54
r=3
2, 6, 18, 54
y=(2/3)(3)x OR y=2(3)x-1
Next=Previous x 3
f(n)=f(n-1) x 3
f(1)=2
Gabe stacks boxes, starting with 15 boxes in the first layer. Each subsequent layer has 3 fewer boxes than the previous layer. Create a table to show the total number of boxes used for the first 5 layers. Write the explicit and recursive equations.
How to label the table:
x-values -> Layer Number
y-values -> Boxes in Layer
Recursive equation:
Next = Previous - 3
f(n) = f(n-1) - 3
f(1) = 15
Explicit equation:
y = -3(n - 1) + 15 OR y = -3n + 18
Find the missing terms of the arithmetic sequence. Write the explicit and recursive equations.
-12, __, __, 24
d=12
-12, 0, 12, 24
y=12(x-1)-12 OR y=12x-24
Next=Previous+12
f(n)=f(n-1)+12
f(1)=-12
Find the missing terms of the geometric sequence. Write the explicit and recursive equations.
5, __, __, 320
r = 4
5, 20, 80, 320
y = (5/4)(4)x OR y = 5(4)x-1
Next = Previous × 4
f(n) = f(n-1) × 4
f(1) = 5
A plant grows unpredictably. It grows 3 cm in the first week, then 5 cm in the second week, and then 4 cm in the third week. Create a table showing the height of the plant at the end of each of the first 5 weeks. Write the explicit and recursive equations.
This pattern is not arithmetic or geometric.
This sequence has no recursive or explicit equations due to varying growth.
Find the missing terms of the arithmetic sequence. Write the explicit and recursive equations.
7.5, __, __, __, 47.5
d = 10
7.5, 17.5, 27.5, 37.5, 47.5
y = 10(x - 1) + 7.5 OR y = 10x - 2.5
Next = Previous + 10
f(n) = f(n - 1) + 10
f(1) = 7.5
Find the missing terms of the geometric sequence. Write the explicit and recursive equations.
128, __, __, 2
r = 0.25 OR r=1/4
128, 32, 8, 2
y = 128(0.25)x-1 OR y=512(0.25)x
Next = Previous × 0.25
f(n) = f(n-1) × 0.25
f(1) = 128
Maria saves $5 in the first week and doubles her savings each subsequent week. Create a table to show how much money she saves each week for 5 weeks. Write the explicit and recursive equations.
How to label the table:
x-values → Week
y-values → Amount of Money Saved
Recursive equation:
Next = Previous × 2
f(n) = f(n-1) × 2
f(1) = 5
Explicit equation:
y = 5(2)x-1 OR y = 2.5(2)x
Find the missing terms of the arithmetic sequence. Write the explicit and recursive equations.
-100, __, __, __, __, 250
d=70
-100, -30, 40, 110, 180, 250
y = 70(x - 1) - 100 OR y = 70x - 170
Next = Previous + 70
f(n) = f(n - 1) + 70
f(1) = -100
Find the missing terms of the geometric sequence. Write the explicit and recursive equations.
1, __, __, 343
r = 7
1, 7, 49, 343
y = 1(7)x-1 OR y=(1/7)(7)x
Next = Previous × 7
f(n) = f(n-1) × 7
f(1) = 1
A pizza is cut into slices. The first pizza has 16 slices, and each subsequent pizza has half the slices of the previous pizza. Create a table to show the number of slices in the first 5 pizzas. Write the explicit and recursive equations.
How to label the table:
x-values → Pizza Number
y-values → Slices
Recursive equation:
Next = Previous × 0.5
f(n) = f(n-1) × 0.5
f(1) = 16
Explicit equation:
y = 16(0.5)n-1 OR y = 32(0.5)x
Find the missing terms of the arithmetic sequence. Write the explicit and recursive equations.
-1500, __, __, __, __, __, __, 750.5
d=312.5
-1500, -1187.5, -875, -562.5, -250, 62.5, 375, 750.5
y = 312.5(x - 1) - 1500 OR y = 312.5x - 1812.5
Next = Previous + 312.5
f(n) = f(n - 1) + 312.5
f(1) = -1500
Find the missing terms of the geometric sequence. Write the explicit and recursive equations.
0.5, __, __, __, 171.5
r = 3.5
0.5, 1.75, 6.125, 21.4375, 171.5
y=(0.5/3.5)(3.5)x OR y=0.5(3.5)x-1
Next = Previous × 3.5
f(n) = f(n-1) × 3.5
f(1) = 0.5
Lucas is tracking his fuel consumption for a road trip. He starts with 100 gallons of fuel in the first week and finds that his fuel consumption increases by a factor (common ratio) of 0.75 each subsequent week due to more efficient driving. Create a table to show the total fuel consumed over the first 5 weeks. Write the explicit and recursive equations.
Round to the nearest hundredth.
How to label the table:
x-values → Week
y-values → Fuel Consumed (gallons)
Recursive equation:
Next = Previous × 0.75
f(n) = f(n-1) × 0.75
f(1) = 100
Explicit equation:
y = 100(0.75)x-1 OR y=133.33(0.75)x