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).]

Question

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

Answer 1

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:
\[ a_{100} = 3 \times 2^{99} \]