## A linear number sequence (aka arithmetic sequence) is an ordered set of numbers which has a common (constant) difference between consecutive terms.

Consider this linear number sequence: `2, 9, 16, 23, 30, 37, 44, 51, ...`

.

### Term

Each number in a sequence, separated by commas, is called a term of this sequence. The first term is called `T`

, followed by _{1}`T`

, _{2}`T`

, and so on._{3}

### Term Value

In a linear number sequence, the term value is the number value of one term. In above example the term value of `T`

._{6} = 37

### Common Difference

The value added between each consecutive term is called the common difference and is always constant in any linear number sequence. We use the letter `d`

to represent the common difference. The common difference can be a positive or negative value.

In above example, the common difference equals 7.

### Finding the Next Term

The rule for finding the next term is to add `d`

(common difference) to the previous term:

`T`

._{n}_{+1} = T_{n} + d

In above example, the rule for finding the next term is to add 7 (common difference) to the previous term, e.g.

`T`

._{9} = T_{8} + 7 T_{9} = 51 + 7 T_{9} = 58

### Finding the n^{th} Term

The n^{th} term (`T`

) of a linear number sequence allows to calculate any term of the sequence:_{n}

`T`

._{n} = d × n + T_{1} - d

We can now work out any term for above example. E.g. the 40^{th} therm:

`T`

._{40} = 7 × 40 + 2 - 7 T_{40} = 280 + 2 - 7 T_{40} = 275

### Graphing Linear Number Sequences

We can graph the term on the x axis and the term value on the y axis. Joining all the points will result a linear (straight) line.

Graphing above example: