Basic Concepts

• A Linear Sequence is a sequence where the difference between two consecutive terms is constant.
• The term-to-term rule can be used to find subsequent terms.
• The n-th term of a sequence is a formula that gives the position of a term in a sequence.

Identifying the nth Term

• To identify the nth term of a linear sequence, one must find the common difference.
• The Common Difference is found by subtracting each preceding term from the following term.

Forming nth Term

• To form the nth term of a sequence, identify the common difference and the first term.
• The nth term of a linear sequence can be written in the form `an + b`, where `a` is the common difference and `b` is a constant.
• `a` is often the multiplier in the term-to-term rules, while `b` is the starting number of the sequence.

Using nth Term

• The nth term can be used to find any term in a sequence without having to know the previous terms.
• Simply replace `n` with the position of the term you are trying to find.
• For instance to find the 10th term, replace `n` with 10 in the formula `an + b`.

Testing nth term

• If you have found the nth term, you can verify it by trying it on one or more terms in the sequence.
• If the formula gives the correct output, then the nth term is very likely correctly identified.

Understanding Problem Solving with nth Term

• Often various problems will make use of the nth term, such as finding the sum of the first n terms.
• Read these problems carefully to identify and understand what is required.

Students must understand that identifying the `n-th term` of a sequence is crucial as it enables you to generate any term in that sequence and helps with understanding the characteristics of the sequence.