Write the sequence in its general form. This form should have an "x" variable in it. For example, 1/2^x is a proper sequence.
Write a new sequence, replacing "x" with "x + 1." This sequence represents a "jump forward" by one in the original sequence. You will be comparing these two sequences to find the ratio. For the previous example, this step would yield 1/2^(x + 1).
Divide the second sequence by the original. You do not need to simplify, as the TI-83 will do it for you after you input it into the calculator. For the example, write "[1/2^(x+1)]/[1/2^x]." This is the general sequence ratio that you will use input in the TI-83.
Open the "List" menu. Press "2nd" followed by "stat." The "List" menu will appear.
Choose "Ops" from the list menu. Scroll down to "Ops" and hit "Enter."
Select the command "Seq." Highlight "Seq" and hit "Enter." You will be brought to the main screen and a command "Seq(" will appear.
Enter the general sequence ratio, followed by a comma. After "Seq(" input the terms for the sequence. For the previous example, you would type "(1/2^(x+1))/(1/2^x)" and then press the "," button on your calculator when finished.
Enter the variable, "x," followed by a comma. Press the "x,t,theta,n" button on the TI-83, followed by the "," button.
Enter the range of values for which you want the TI-83 to compute the sequence ratio for. Enter the initial value for "x," followed by a comma, the final value for "x" and the closing parentheses. For example, if you want to compute the sequence ratio out from 1 until 20, you would type "seq((1/2^(x+1))/(1/2^x),x,1,20)" as the full command.
Tell the TI-83 to compute the values of the sequence ratio. Hit "Enter" after double-checking the command you have entered. The output will be the sequence ratio.