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Math 25
 Patterns Homework 

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S1. Triangular tables are placed in a row to seat more people. One table has 3 seats. Two tables have 4 seats. Create a formula where we put in the number of tables (as n) and get out the number of seats (as y).

y = n + 1 y = n + 2 y = 2n + 1 y = 2n + 2 y = n × 2

S2. Now we switch to square tables. We still make a row of tables to seat more people. One table has 4 seats. Two tables have 6 seats. Create a formula where we put in the number of tables (as n) and get out the number of seats (as y).

y = n + 3 y = 2n + 1 y = 2n + 2 y = (n + 1)2 y = 3n + 1

S3. This shape is sort of like a V or W that gets wider with more wiggles. What is the pattern for how many squares are in each row?

y = n + 2 y = 2n + 1 y = 2n + 2 y = n × 3 y = n2

S4. How about this extra-wide plus shape? What is the pattern for how many squares are in each row?

y = 5n − 1 y = 6n − 1 y = 6(n − 1) − 1 y = 6(n − 1) + 5

S5. This shape looks somewhat like the stand that holds up a road construction sign. With each step it gets longer in each direction. What is the pattern for how many cubes are in each row?

y = 5n + 1 y = 5n − 4 y = 5(n − 1) + 1 y = 5(n − 1) − 4

S6. There are many versions of an old story about the inventor of the game of chess. One version appears below. On which day will the total grains of rice exceed 3 million?

Day 21 Day 22 Day 23 Day 24