Patterns, Functions, & Algebra – Patterns (Notes)

Name Date

I can … / Essential Question:
Key Concepts / Notes
Sequence
  • Definition
Arithmetic sequence
  • Definition
  • Example
Geometric sequence
  • Definition
  • Example
Section #1 – Patterns/Sequences in Tables
  1. The owner of a sporting goods store is following a pattern to arrange baseballs into 7 rows for a wall display. The table to the right shows the number of baseballs in the first four rows of this pattern.
How many baseballs are in the seventh row of this pattern?
  1. A grocery store has a triangular pyramid of soup cans on display. Steven counts the number of cans in each of the top five layers. Each successive layer continues following the same pattern.
The display has 10 layers. How many cans are in the 10th layer?
  1. The table to the right contains the results of a biology experiment.
Assuming the pattern shown in the table continues, what is the value of b?
Section #2 – Patterns/Sequences with Rows
  1. The first four rows of a number array are shown to the right.
What number will be at the far right end of row 7?
  1. The first five rows of a number array are shown to the right.
What is the sum of the numbers in row 8?
Section #3 – Extended Response Questions
  1. Nancy decided to breed gerbils to sell to a pet store. She started with 2 gerbils and determined that they should quadruple in number every 4 months. Nancy sold all of the gerbils at the end of 1 year.
How many gerbils did Nancy sell to the pet store?
  1. A pattern of shaded and un-shaded squares is shown to the right.
a)Find a formula for the number of shaded number of squares in the “n”th figure.
b)Find the number of shaded squares in the 50th figure. Show your work or explain your answer.
  1. Maria is making a quilt. She has a large piece of fabric that is 0.02 millimeters thick. The fabric is cut in half, and one piece is placed on top of the other to make a pile. The pile is cut half, and then one half is placed on top of the other to make a higher pile.
Continuing this process, what would the thickness of the pile be after the 4th cut and piling? /
Summary, Reflection, & Analysis

Patterns, Functions, & Algebra – Patterns (Exercise)

Name Date

  1. In the sequence …, 1, 4, 16, 64, … , determine what the pattern is and then find the next 3 terms.
  1. In the sequence …, 4, - 1, - 6, - 11, … , determine what the pattern is and then find the next 3 terms.
  1. Suppose the pattern of dots continues infinitely with more dots being added at each step. Determine a formula for the number of dots for the “n”th step. How many dots will be in step 14?
  1. A large corporation uses a telephone chain to notify employees of company closings due to bad weather. The plant manager calls 5 people in the first round of the telephone chain. Each of those people calls 5 other people in the second round of the telephone chain. If the pattern continues, how many employees are called in the 4th round of the telephone chain?
  1. The depth of a lake is measured at the same location and on the same day every year for a number of years. The table below shows the measurements.

If the pattern continues, what will be the depth

of the lake in 2003?

  1. Last spring, the employees of an Akron tire company contributed to a local charity. The graphic represents the total dollar contributions as of several dates in April.

Determine on what date the charity could have expected

to reach its goal of $1,000 if the pattern of donations remains

about the same. Provide an explanation as to how you arrived

at that answer.

  1. The first five rows of a number array are shown below.

What is the sum of the numbers in row 9?

  1. Mr. Abraham was given a special offer by the bank. They told him that if he opened a savings account and put $1 on it, they would promise that it would triple at the end of every year. Assuming this pattern continues, how many years will it take Mr. Abraham to turn his $1 into $50,000?