An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula

**a _{n} = d (n - 1) + a1 **

where d is the common difference between consecutive terms and a1 is the first term in the sequence.

**Examples: **For the sequence

1, 4, 7, 10, 13, 16…….

This sequence has a difference of 3 between each number. Therefore,

D = 3 and a1 = 1

Thus, the formula for the series is

a_{n} = 3(n – 1) + 1

= 3n – 3 + 1

a_{n} = 3n – 2

The sum of an infinite arithmetic sequence is either ∞ , if

d > 0 , or - ∞ , if d < 0 .

There are two ways to find the sum of a finite arithmetic sequence. In the first method, the value of the first term **a1** should be known and the value of the last term **an** as well. Then, the sum of the first **n **terms of the arithmetic sequence is

**S _{n}**

**2**

To use the second method, you must know the value of the first term **a 1** and the common difference **d **. Then, the sum of the first **n** terms of an arithmetic sequence is

**S _{n}**

** 2**

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