Understanding sequences is important, especially when we look at two types: finite and infinite sequences.

Finite Sequences:

These are sequences that have a set number of terms.

For example, the even numbers from 2 to 10 form a finite sequence:
$2, 4, 6, 8, 10$.

You can count these terms, and you see that it stops after 5 numbers.

Infinite Sequences:

On the other hand, infinite sequences go on forever.

A simple example would be the sequence of natural numbers:
$1, 2, 3, 4, \ldots$.

As you can tell, it just keeps going without an end.

Key Terms:

• Terms: These are the parts of a sequence. For instance, in the sequence above, $2$ is one term.

• Nth Term: This refers to the term in the sequence that is at position $n$. For the even numbers, we can write the nth term as $2n$.

• General Term: This is a formula that tells you the $n$th term for any term in the sequence. For the infinite sequence of odd numbers, the general term is $2n - 1$.

Knowing the differences between finite and infinite sequences helps us understand and analyze them better!