Arithmetic Sequences

A sequence is a set of numbers in a specific order.The numbers in the sequence are called  terms. The difference between terms in the sequence is called the common difference.

For example, in the sequence 5, 9, 13, 17, 21, the common difference is 4.

An arithmetic sequence is a numerical pattern that increases or decreases at a constant rate called the common difference.

To find the nth term in an arithmetic sequence, use the formula:

 a_n = a₁ + ( n - 1 ) d

where    a_n  = the nth term, a₁ = the first term, and d = the common difference.

In the example above, the value of the 21st term is:

a₂₁ = 5 + (21 - 1)4 = 5 + (20)4 = 5 + 80 = 85