Arithmetic and Geometric Series

Notation:

Number of terms in the series: n

First term: a1

Nth term: an

Sum of the first n terms: Sn

Difference between successive terms: d

Common ratio: q

Sum to infinity: S

Arithmetic Series Formulas:

an=a1+(n1)d
ai=ai1+ai+12
Sn=a1+an2n
Sn=2a1+(n1)d2n

Geometric Series Formulas:

an=a1qn1
ai=ai1ai+1
Sn=anqa1q1
Sn=a1(qn1)q1
S=a11q,(for 1<q<1)