Geometric Sequences and Series

Lesson · Beginner

Algebra: Sequences & Series

a_n=a_1r^{n-1},\qquad n\ge 1

a_n^2=a_{n-1}a_{n+1}

S_n=a_1+a_1r+a_1r^2+\cdots+a_1r^{n-1} =\frac{a_1(r^n-1)}{r-1}

|r|<1:\qquad S_\infty=a_1+a_1r+a_1r^2+\cdots =\frac{a_1}{1-r}