How to Use Geometric Sequence Calculator
The Geometric Sequence Calculator handles sequences that change by multiplication. Enter the first term, common ratio, and number of terms to find an and Sn. The Geometric Sequence Calculator also includes reverse modes for common ratio or term number when the known values allow it.
Formula & Theory — Geometric Sequence Calculator
The Geometric Sequence Calculator uses:
a_n = a_1*r^(n-1)
S_n = a_1(1-r^n)/(1-r), r != 1
S_n = n*a_1, r = 1
The common ratio r controls growth, decay, sign alternation, or constant behavior. Special cases such as r=1 are handled separately.
Use Cases for Geometric Sequence Calculator
Use the Geometric Sequence Calculator for algebra, exponential patterns, finance examples, population models, repeated scaling, and sequence homework. It is useful whenever each term is created by multiplying the previous term by the same ratio.