Question

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

Answer 1

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))`.