# Lesson 9Geometric MeaniesSolidify Understanding

For each set of sequences, find the first five terms. Then compare the growth of the arithmetic sequence and the geometric sequence. Which grows faster? When?

### 1.

Arithmetic sequence: , common difference

Geometric sequence: , common ratio

Arithmetic

Geometric

#### b.

Which value will be greater, or ? Why?

### 2.

Arithmetic sequence:

Geometric sequence:

Arithmetic

Geometric

#### b.

Which value will be greater, or ? Why?

### 3.

Arithmetic sequence:

Geometric sequence:

Arithmetic

Geometric

#### b.

Which value will be greater, or ? Why?

### 4.

Arithmetic sequence:

Geometric sequence:

Arithmetic

Geometric

#### b.

Which value will be greater, or ? Why?

### 5.

Arithmetic sequence: , common difference

Geometric sequence: , common ratio

Arithmetic

Geometric

#### b.

Which value will be greater, or ? Why?

### 6.

Considering arithmetic and geometric sequences, would there ever be a time that a geometric sequence does not outgrow an arithmetic sequence in the long run as the number of terms in the sequences becomes really large? Explain.

## Set

Each of the given tables represents a geometric sequence. Find the missing terms in the sequence and create the explicit and recursive equations. Show your method.

### 7.

#### a.

Table 1

 $x$ $y$ $1$ $2$ $3$ $5$ $20$

#### b.

Explicit equation:

#### c.

Recursive equation:

### 8.

Table 2

#### b.

Explicit equation:

#### c.

Recursive equation:

### 9.

Table 3

#### b.

Explicit equation:

#### c.

Recursive equation:

### 10.

Table 4

#### b.

Explicit equation:

#### c.

Recursive equation:

## Go

Use the given information to write the explicit equation for each geometric sequence.

, common ratio:

### 14.

Which of the geometric sequences in problems 11–13 has the greatest value at ? Why?