# What is meant by the sum of an arithmetic sequence?

Aug 30, 2015

The sum of an arithmetic sequence is a sum of a finite number of consecutive terms of an arithmetic sequence starting from ${a}_{1}$ ending at ${a}_{n}$

#### Explanation:

In arithmetic sequence there is nothing like a sum of a (whole) sequence, because it would have to be $+ \infty$. On the other hand you can calculate (that is what you probably meant) a sum of $n$ terms of a sequence which can be written as:

${S}_{1} = {a}_{1}$
${S}_{2} = {a}_{1} + {a}_{2}$
${S}_{3} = {a}_{1} + {a}_{2} + {a}_{3}$
and so on.

In general ${S}_{n} = {a}_{1} + {a}_{2} + {a}_{3} + \ldots + {a}_{n}$, and such sum can be calculated using formula:

${S}_{n} = \frac{{a}_{1} + {a}_{n}}{2} \cdot n$