Is this formula for a arithmetic sequence? #sum_(k=0)^(k=n-1)ar^k=a((1-r^n)/(1-r))#

1 Answer
Aug 13, 2016

Answer:

The formula is for sum of a geometric sequence and not arithmetic sequence. See details below.

Explanation:

This formula is not about arithmetic sequence, but is for a geometric sequence.

Note that sequence starts from #k=0# for which first number is just #a×r^0=a#.

Then changing #k# from #1# to #(n-1)#, we get last term i.e. #n^(th)# term.

The right hand side gives the value of sum of the sequence for #r<1#. In case #r>1#, this can be put as #a((r^n-1)/(r-1))#.