General terms are really important when we talk about sequences. They help us explain patterns or rules in a simple way.

1. What Are the Types of Sequences?

• Finite Sequences: These have a set number of terms. For example, the sequence $1, 2, 3, \ldots, n$ has $n$ terms. That means it stops at a certain number.

• Infinite Sequences: These go on forever. An example would be $1, 1/2, 1/3, \ldots$ This keeps going without an ending.

2. Important Terms to Know:

• Terms: These are the individual parts of a sequence. In the sequence $2, 4, 6, \ldots$, the first term is $2$.

• Nth Term: This is the term that is in the $n$th position. For example, if the sequence is $an = 2n$, then $a_3 = 6$. This means the third term is $6$.

• General Term: This is a formula that tells us how to find the $n$th term. For an arithmetic sequence, the general term is $a_n = a + (n-1)d$, where $d$ is the difference between each term.

Using general terms makes it easier to do math with large sequences. We can make calculations and predictions without writing down every single term. This helps us solve problems more efficiently!