CA O’Brien F15
Sums and Sequences on the TI-83 Plus and TI-84 Plus
Sequences – The seq function
A sequence of numbers is just an ordered list of numbers, for example, {1, 2, 3, 4, 5} or {1, 2, 5, 3, 11, 2, 3}. The “ordered” part simply means
that each term in the sequence is assigned a specific index. In the sequence {1, 1/2, 1/3, 1/4, …}, the second term is 1/2 and the fourth term is
1/4. Sequences can be any length, or even be infinite in length.
Sequences are handled on the TI-83 and TI-84 using the seq function. To reach this function from the home screen, press 2nd STAT ▶ 5.
On newer calculators, a screen will show up which will guide you through entering the function, though in any case the syntax is the same.
First, enter the expression you want, next the variable you’re using, and finally the starting and ending values of your variable. The syntax will
be pasted onto your screen, so press ENTER to evaluate. Note that on some older models, you might have to put quotation marks around the
equation and variable name.
A list containing your sequence will be returned.
Summations – Adding up Terms
A summation is a sum of numbers that are typically defined by a function. For example, saying “the sum from 1 to 4 of n²” would mean
1²+2²+3²+4² = 1 + 4 + 9 + 16 = 30. Sums can also be infinite, provided that the terms eventually get close enough to zero–this is an important
topic in calculus. For example, adding up the sum of 1/n does not converge, whereas the sum of 1/n² converges to π²/6, a rather unexpected
result.
There are a couple of ways to evaluate sums on your calculator. Calculators with newer operating systems actually have a summation
function, which can by reached by pressing MATH 0. With it you can use your arrow keys to select your counting variable (typically X), set the
limits, and enter the expression you want to evaluate.
If your calculator doesn’t have this feature, you can perform the same operation by summing up a sequence: Press 2nd STAT ◀ to reach the
List MATH menu, 5 to select sum, then select the seq function as above. Press ENTER to evaluate.
Adapted from http://www.calcblog.com/sums-sequences-ti83-ti84/