Graphing sequences is a great way to understand how they work, especially when looking at two types: arithmetic and geometric sequences.

Seeing Patterns

When you put the terms of a sequence on a graph, the patterns become much clearer.

For example, an arithmetic sequence like $a_n = 3n + 2$ makes a straight line. This shows that the sequence increases at a steady rate.

On the other hand, a geometric sequence like $g_n = 2^n$ creates a curve that goes up quickly. This shows that the numbers grow very fast.

Spotting Important Features

Graphs can help us see important traits, like:

• Straight-line growth in arithmetic sequences.
• Rapid growth in geometric sequences.

Real-Life Examples

Let’s see what happens when we graph the first five terms of each type of sequence:

• For Arithmetic: the terms are $2, 5, 8, 11, 14$. This will make a straight line.
• For Geometric: the terms are $2, 6, 18, 54, 162$. This looks like a steep curve going up.

In summary, graphing sequences not only helps us see the terms clearly but also helps us understand their unique properties and behaviors better.