Geometric Sequences as Exponential Functions

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This topic isn't really tested, however, it is important to get a basic understanding

Multiple Choice

The next term of the geometric sequence

4, 16, 64, ...

is

• 256

• 132

• 120

• 150

Multiple Choice

What is a₅ in the sequence defined as follows?
a_n = 5 ⋅ 2^(n-1) 

• a₅ = 160

• a₅ = 40

• a₅ = 10

• a₅ = 80

Multiple Choice

A sequence can be generated by using $$a_n=4a_{\left(n-1\right)}$$  where  $$a_1=6$$  and  $$n$$  is a whole number greater than 1.  What are the first four terms in the sequence?

• 6, 24, 96, 384

• 6, 10, 14, 18

• 6, 20, 100, 500

• 6, 20, 76, 300

Multiple Choice

Write the explicit 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

Multiple Choice

You have $10 in you bank account.  It doubles every month.  How much money will you have after 5 months?

• $50

• $35

• $320

• $250

Multiple Choice

Given the sequence:

125, 25, 5, ....

What is the zeroth term?

• 5

• 625

• 250

• 125

Multiple Choice

Write the explicit equation for the geometric sequence: 15, 45, 135, . . . ?

• $$t\left(n\right)=3\left(5\right)^n$$

• $$t\left(n\right)=5\left(3\right)^n$$

• $$t\left(n\right)=5n+3$$

• $$t\left(n\right)=3n+5$$

Multiple Choice

Write the explicit equation for the geometric sequence:

10, 20, 40, 80, ...

• $$t\left(n\right)=5\left(2\right)^n$$

• $$t\left(n\right)=2\left(5\right)^n$$

• $$t\left(n\right)=2\left(10\right)^n$$

• $$t\left(n\right)=10\left(2\right)^n$$