# n-th Terms of Linear Sequences

## n-th Terms of Linear Sequences

# Understanding Linear Sequences

Linear sequences can also be called arithmetic sequences. They follow a simple pattern of adding or subtracting a consistent value.

- A
**linear sequence**has a constant difference between terms - this is often referred to as the**common difference** - The common difference can be found by subtracting any term from the term that follows it.
- The
**n-th term**of a linear sequence: This is a formula that allows you to find any term in the sequence without listing all the preceding terms.

# Identifying the n-th Term

- The n-th term of a linear sequence can be found using the formula
**a + (n - 1)d**, where “a” is the first term in the sequence, “d” is the common difference, and “n” is the term number in the sequence. **Example:**For the linear sequence 5, 7, 9, 11, …,**a = 5**and**d = 2**.The n-th term is therefore**5 + (n - 1)2**. Simplifying, we get**2n + 3**.

# Application of the n-th Term

- Once you have found the n-th term, you can find any term in the sequence.
**Example**: If the n-th term formula is 3n + 2, the 10th term of the sequence is**3*10 + 2 = 32**.

Remember that understanding the concept of n-th term is useful not just for finding terms in a sequence, but also for determining whether a number is part of a sequence.