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

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Answer 1 · 2016-08-13T14:00:27

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

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 $a((r^n-1)/(r-1))$ .

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