Question

1. Graph your arithmetic sequence on a coordinate grid (a sheet of graph paper).

2. Write a linear function to represent your arithmetic sequence. Show that it has
the same structure as your explicit formula from

3. Graph your geometric sequence on a coordinate grid (a sheet of graph paper).

4. Write an exponential function to represent your geometric sequence. Make sure it has the same structure as the explicit formula “a_100 = 3 x 2^99”.

Make your answers as short as possible
Answer each question seperately

Answer 1

### 1. Graph of Arithmetic Sequence
To graph an arithmetic sequence, you need specific terms. For example, let's use the sequence \(2, 5, 8, 11, 14\).

1. Plot the following points:
- (1, 2)
- (2, 5)
- (3, 8)
- (4, 11)
- (5, 14)

The points will form a straight line.

### 2. Linear Function Representation
The explicit formula for the arithmetic sequence is \(a_n = 2 + (n-1) \cdot 3\).

This can be rewritten in linear function form as:
\[ f(n) = 3n - 1 \]
Thus, both formulas represent the same relationship.

### 3. Graph of Geometric Sequence
For the geometric sequence \(3, 6, 12, 24, 48\):

1. Plot these points:
- (1, 3)
- (2, 6)
- (3, 12)
- (4, 24)
- (5, 48)

The points will show an exponential growth curve.

### 4. Exponential Function Representation
The explicit formula for the geometric sequence is \(a_n = 3 \cdot 2^{n-1}\).

We can express it in exponential function form:
\[ g(n) = 3 \cdot 2^{n-1} \]
This structure matches that of \(a_{100} = 3 \cdot 2^{99}\).