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

Aug 13, 2016

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 $\left(n - 1\right)$, we get last term i.e. ${n}^{t h}$ 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 $a \left(\frac{{r}^{n} - 1}{r - 1}\right)$.