# Using n-th Terms of Linear Sequences

## Using n-th Terms of Linear Sequences

# 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.