Knowledge Base

Solution 28870: Calculating the Summation of a Geometric Sequence Using the TI-Nspire™ Family Products.

How do I calculate the summation of a geometric sequence using the TI-Nspire family products?

To calculate the summation of a geometric sequence using the TI-Nspire family handheld and computer software, the "summation (å)" function must be used. If the summation requires a "step" value, then the "sum" and "seq"  functions must be used together. For help with calculations using either method, follow the examples below. Texas Instruments recommends all TI-Nspire family users update the handheld and computer software to the latest operating system. More information on the latest operating system can be found at the TI-Nspire family latest software website.

Example: Calculate the summation of the geometric sequence x² as x goes from 1 to 5.

1) Press [home] [1] to create a New Document. If prompted to save the existing document, choose "Yes" or "No". Press [1] to insert the Calculator application.
2) Press [menu] [4] [3] to select the "Sum" function. This will paste the summation (å) function into Calculator application.

3) The cursor will blink in the lower-left box. Input "x", press [tab] to move to the box to the right, then input "1".
4) Press [tab] to move to the top box. Input "5" and press [tab]. The cursor will move to the outside of the summation (å) function.
5) Input x² and press [enter]. The handheld will display 55 since 1² + 2² + 3² + 4² + 5² = 55.

Please Note: The next example is also calculated using the Calculator application.

Example: Calculate the summation of the geometric sequence x² as x goes from 4 to 16 with a step value of 4.

1) Press [menu] [6] [3] [5] to paste the sum function into the Calculator application. Press [menu] [6] [4] [5] to paste the seq function into the Calculator application.

2) Inside the second set of parentheses, input "x²,x,4,16,4" and press [enter]. The handheld will return 480 since 4² + 8² + 12² + 16² = 480.

Please see the TI-Nspire family guidebooks for additional information.