Activity: Patterns Lab
A recursive formula tells you how to get the next term in the sequence. But what if you wanted the 100th term? Do you
want to do the formula 100 times? In this activity you are looking for a relationship between the term and the term
number.
Using the given diagrams, list the first three terms, the 10th term and the 100th term. Then write a formula to find the
nth term based on the term number n.
NOTE: The formula you are writing is not a recursive formula that will be used repeatedly, but instead a formula that
will produce the results in one action.
Cubes in Tower Cubes in All
1.
The building with one cube
for its tower takes 6 cubes to build.
The building with two cubes
for its tower takes 7 cubes to build.
The building with 3 cubes for its
tower takes 8 cubes to build.
1 6
2 7
3
10
100
n
2.
A kite with 1 cube for its tail
takes 10 cubes to build.
A kite with 2 cubes for its tail
takes 11 cubes to build.
Cubes in Tail Cubes in All
1 10
2 11
3
10
100
n
3.
A tower with one floor takes 3 cubes to build.
Floors Cubes in All
1
2
A tower with 2 floors takes 6 cubes to build.
A tower with 3 floors takes 9 cubes to build.
3
10
100
n
4.
For one car, it takes 5 cubes for a carport.
Cars Cubes in Carport
1 5
2 10
For two cars, it takes 10 cubes for a carport.
3 15
10
For three cars, it takes 15 cars for a carport.
100
n
Layers Bricks
5.
A well with one layer takes 8 bricks to build.
1
2
A well with 2 layers takes 16 bricks to build
3
10
A well with 3 layers takes 24 bricks to build
100
n
6.
For 1 cow, it takes 8 cubes to build a fence.
Cars Cubes in Carport
1
2
For 2 cows, it takes 10 cubes to build a fence.
3
10
For 3 cows, it takes 12 cubes to build a fence.
100
n
Arches Cubes in All
7.
One arch takes 7 cubes to build.
Two arches take 11 cubes to build.
1
2
3
Three arches take 15 cubes to build
10
100
n
8.
A building with one window
takes 8 cubes to build.
Windows Shaded Cubes
1
2
A building with 2 windows
takes 13 cubes to build.
3
A building with 3 windows
takes 18 cubes to build.
10
100
n
9.
A chair 2 cubes tall takes 3 cubes to build.
Height of Chair Cubes in All
2
3
A chair 3 cubes tall takes 5 cubes to build.
4
10
A chair 4 cubes tall takes 7 cubes to build.
100
n
Stories Cubes in All
10.
The building 2 stories tall takes
7 cubes to build.
2
3
The building 3 stories tall takes
11 cubes to build.
4
10
The building 4 stories tall takes
15 cubes to build.
11.
100
n
Stories in Tower Cubes in All
The building with towers
3 stories tall takes 11 cubes
to build.
The building with towers
4 stories tall takes 13 cubes
to build.
3
4
5
10
100
The building with towers
5 stories tall takes 15 cubes
to build.
n
Staircase Cubes in All
12.
The first staircase takes 1 cube to build
1
2
3
The second staircase takes 4 cubes to build.
10
100
The third staircase takes 9 cubes to build.
n