What is meant by the sum of an arithmetic sequence?

1 Answer
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 #+oo#. 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+...+a_n#, and such sum can be calculated using formula:

#S_n=(a_1+a_n)/2*n#