Graphing and Writing Geometric Sequences

Determine whether the sequence is arithmetic, geometric, or neither.

• arithmetic

• geometric

• neither

Write the explicit formula for the geometric sequence.

• a_n = 10(2)^n-1

• a_n = 2(10)^n-1

• a_n = 10(2)ⁿ

• a_n = 2(10)ⁿ

Describe and correct the error shown to the right that a student made when writing a recursive formula from an explicit formula.

Write the formula for the geometric sequence.

• a_n = 4(3)^n-1

• a_n = 3(4)^n-1

• a_n = -4(3)^n-1

• a_n = 3(-4)^n-1

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

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.

A geometric sequence with

r>0

is​ a(n)​ (a)   function.

• exponential

• cubic

• linear

• quadratic

Create the formula for the geometric sequence:
1, 4, 16, 64...

• a_n = 3^n-1

• a_n = 2^n-1

• a_n = 5^n-1

• a_n = 4^n-1

Create the formula for the geometric sequence:
-2, 10, -50, 250...

• a_n = 2(-5)^n-1

• a_n = -2(-5)^n-1

• a_n = -2(5)^n-1

• a_n = 2(5)^n-1