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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

1 answer

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 \(a_{100} = 3 \cdot 2^{99}\).