Arithmetic and Geometric Sequences and Series

Arithmetic Series:


Find ana_{n}

an=a1+d(n−1)a_{n}=a_1+d\left(n-1\right)


Find SnS_{n}

Sn=n2(a1+an)S_{n}=\frac{n}{2}\left(a_1+a_{n}\right)



Geometric Series:


Find ana_{n}

an=a1rn−1a_{n}=a_1r^{n-1}


Find SnS_{n}

Sn=a1−a1rn1−rS_{n}=\frac{a_1-a_1r^{n}}{1-r}


Find S∞S_{\infty}

S∞=a11−rS_{\infty}=\frac{a_1}{1-r}