Geometric Series

This series of interactive excel sheets help investigate geometric series and progressions.

The first sheet generates the terms of a geometric progression, for |r| ≥ 1, and the value of a further term. A new sequence can be generated at the click of a button.

The second interactive sheet demonstrates the effect of changing the common ratio for a geometric series. It displays two graphs which plot the value and sum of the first twenty terms of a geometric series with first term 0.8 and a changeable common ratio, for |r| ≥ 1.

The third sheet generates the terms of a geometric progression, where |r| < 1 and given as a decimal, and the value of a further term. A new sequence can be generated at the click of a button.

Similarly the forth sheet generates a geometric progression, however the common ratio can be set from a list of common fractions.

The following sheet shows how a proof of the formulae for the sum to infinity can be deduced from the sum of the first n terms.

The next interactive sheet, similar to the second sheet, demonstrates the effect of changing the common ratio for a geometric series for |r| < 1. It displays two graphs which plot the value and sum of the first twenty terms of a geometric series with first term 0.8 and a changeable common ratio.

The next two sheets contain table of six changeable geometric progressions and invites users to complete the missing values that can then be revealed.

The file also contains two printable A4 worksheets on number sequences and their formulae and a further worksheet on recurrence relations.

Note
This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.