Question
1. Graph your arithmetic sequence on a coordinate grid (a sheet of graph paper). [question answered, (1,2), (2,5), (3,8) (4,11), and (5,14).]
2. Write a linear function to represent your arithmetic sequence. Show that it has
the same structure the explicit formula “a_100 = 3(100) - 1 = 300 - 1 = 299”.
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
2. Write a linear function to represent your arithmetic sequence. Show that it has
the same structure the explicit formula “a_100 = 3(100) - 1 = 300 - 1 = 299”.
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
Answers
GPT-4o mini
### 1. Graph your arithmetic sequence on a coordinate grid
The points for your arithmetic sequence are: (1,2), (2,5), (3,8), (4,11), and (5,14).
### 2. Write a linear function to represent your arithmetic sequence
The arithmetic sequence can be represented by the linear function:
\[ f(n) = 3n - 1 \]
To show that it has the same structure as the explicit formula:
\[ a_{100} = 3(100) - 1 = 300 - 1 = 299 \]
### 3. Graph your geometric sequence on a coordinate grid
Assuming the geometric sequence is not specified, let's consider an example with the first few terms as (1, 3), (2, 6), (3, 12), (4, 24), and (5, 48).
### 4. Write an exponential function to represent your geometric sequence
Assuming the ratio is 2, the exponential function can be represented as:
\[ f(n) = 3 \times 2^{(n-1)} \]
To demonstrate the structure:
\[ a_{100} = 3 \times 2^{99} \]
The points for your arithmetic sequence are: (1,2), (2,5), (3,8), (4,11), and (5,14).
### 2. Write a linear function to represent your arithmetic sequence
The arithmetic sequence can be represented by the linear function:
\[ f(n) = 3n - 1 \]
To show that it has the same structure as the explicit formula:
\[ a_{100} = 3(100) - 1 = 300 - 1 = 299 \]
### 3. Graph your geometric sequence on a coordinate grid
Assuming the geometric sequence is not specified, let's consider an example with the first few terms as (1, 3), (2, 6), (3, 12), (4, 24), and (5, 48).
### 4. Write an exponential function to represent your geometric sequence
Assuming the ratio is 2, the exponential function can be represented as:
\[ f(n) = 3 \times 2^{(n-1)} \]
To demonstrate the structure:
\[ a_{100} = 3 \times 2^{99} \]