Sequences calculator

The two most important sequences. An arithmetic sequence has a constant difference $r$ between terms:

$a_n=a_1+(n-1)r \qquad S_n=\frac{(a_1+a_n)\,n}{2}$

A geometric sequence has a constant ratio $q$:

$a_n=a_1\cdot q^{\,n-1} \qquad S_n=a_1\cdot\frac{q^{\,n}-1}{q-1}\ (q\neq1)$

When $|q|<1$, a geometric sequence has a finite sum of the infinite series $S_\infty=\dfrac{a_1}{1-q}$. Enter $a_1$, $r$ or $q$ and $n$ — you get $a_n$, $S_n$, the list of first terms, and the monotonicity.