Geometric Sequence and Series JavaScript Simulation Applet HTML5
A geometric sequence is a number sequence of the form
,
where a is the first term of the sequence, and r is a constant, also called the common ratio.
On the other hand, a geometric series is written as the sum of the terms in the sequence as such:
,
where the terms of the sum continue indefinitely.
This simulation (link here) sets the first term of the sequence to be 1, and the common ratio in the simulation is denoted as a. From here on, a will denote the common ratio used in the simulation.
There are 3 graphs in the simulation. The leftmost graph plots the first 20 terms of the geometric sequence, the center graph plots the partial sum of those 20 terms, and the rightmost graph plots the limit of the series as the common ratio a changes.
The red arrow in the center graph denotes the limit of the partial sums as the number of terms approach infinity.
The common ratio, a, can be changed using the slider at the top of the simulation, and the field to the right of the slider displays the limit that the sum approaches (1/(1-a) for |a|<1).
The combo box allows you to toggle the array display between showing the terms of the sequence and the partial sums up to a certain term.
,where a is the first term of the sequence, and r is a constant, also called the common ratio.
On the other hand, a geometric series is written as the sum of the terms in the sequence as such:
,where the terms of the sum continue indefinitely.
This simulation (link here) sets the first term of the sequence to be 1, and the common ratio in the simulation is denoted as a. From here on, a will denote the common ratio used in the simulation.
There are 3 graphs in the simulation. The leftmost graph plots the first 20 terms of the geometric sequence, the center graph plots the partial sum of those 20 terms, and the rightmost graph plots the limit of the series as the common ratio a changes.
The red arrow in the center graph denotes the limit of the partial sums as the number of terms approach infinity.
The common ratio, a, can be changed using the slider at the top of the simulation, and the field to the right of the slider displays the limit that the sum approaches (1/(1-a) for |a|<1).
The combo box allows you to toggle the array display between showing the terms of the sequence and the partial sums up to a certain term.
