Arithmetic and Geometric Sequence Word Problems

Carey is organizing her books and putting them on shelves. She put 2 books on the first shelf, 8 books on the second shelf, 32 books on the third shelf, and 128 books on the fourth shelf. What kind of sequence is this?

• Geometric

• Arithmetic

• Both

• Neither

Which sequence type, and common ratio/difference is correct for the table?

• arithmetic

  common ratio = 2

• geometric

  common ratio = 2

• arithmetic

  common difference = 2

• geometric

  common difference = -2

Find the explicit formula for the sequence shown in the graph.

Which type of sequence is shown in the graph?

• Arithmetic

• Geometric

• Neither

• Arithmetic

• Geometric

Answer explanation

Percentages are almost always Geometric.

• 315

• 330

• 345

• 360

Which type of sequence is shown in the graph?

• Arithmetic

• Geometric

• Neither

Match the following for the prompt: A bacteria colony starts with 5 bacteria and triples every hour.

• 5

• Initial value

• Explicit equation

• 3

• Common ratio

• Recursive equation

Explain how you could use a graphing calculator to determine whether the data in the table to the right represents a geometric sequence.

• Multiply each term by the preceding term to see if there is a common ratio.

• Divide each term by the preceding term to see if there is a common ratio.

• Subtract each term from the preceding term to see if there is a common difference.

• Add each term to the preceding term to see if there is a common difference.

f(4) = 33 and f(10) = 57. Write a recursive rule for this if the sequence is arithmetic.

• f(1) = 33

  f(n) = f(n-1) + 4

• f(n) = 21 + 4(n-1)

• f(1) = 21

  f(n) = f(n-1) + 4

• f(n) = f(1) + 4