# Lesson 8What Does It Mean?Solidify Understanding

### 1.

Use the Venn diagram to compare and contrast arithmetic and geometric sequences.

For each representation in problems 2 and 3, select all items that connect to it.

 A:$v\left(t\right)=22{\left(1.02\right)}^{t}$ B:Each day Alex is borrowing $10$ from his mom. C:$g\left(n\right)=-10-10\left(n-1\right)$ D:a coordinate plane with a negative sloped linear functionx555101010y–40–40–40–20–20–20202020000 E:a coordinate plane with a positive sloped exponentiation functionx202020404040606060y202020404040606060000 F:a chart. In the x-column the inputs are listed as 5, 6, 7, 8. The y-column outputs are 24.29, 24.78, 25.27, 25.78, respectively.

Connected items:

### 3.

Jose is studying the growth of the economy, and he believes that the rate of growth will be for the next several years. If it has a current value of , how many years will it take to double the value?

Connected items:

## Set

Each of the tables given represents an arithmetic sequence. Find the missing terms in the sequence, show your method, and create the explicit and recursive equations.

Table 1

Explicit:

Recursive:

Table 2

Explicit:

Recursive:

Table 3

Explicit:

Recursive:

Table 4

Explicit:

Recursive:

## Go

Identify the type of sequence and then determine the recursive and explicit equations for each sequence. (If the sequence is not arithmetic or geometric, identify it as neither and don’t write the equations.)

### 8.

, , , ,

#### a.

Arithmetic, geometric, or neither?

#### b.

Recursive equation:

#### c.

Explicit equation:

### 9.

, , , ,

#### a.

Arithmetic, geometric, or neither?

#### b.

Recursive equation:

#### c.

Explicit equation:

### 10.

, , , ,

#### a.

Arithmetic, geometric, or neither?

#### b.

Recursive equation:

#### c.

Explicit equation:

### 11.

(The number of black tiles is the sequence.)

#### a.

Arithmetic, geometric, or neither?

#### b.

Recursive equation:

#### c.

Explicit equation:

### 12.

, , , ,

#### a.

Arithmetic, geometric, or neither?

#### b.

Recursive equation:

#### c.

Explicit equation: