"Sequence" means almost the same as "list". The only difference is that mathematicians also consider infinite sequences, and the word "list" is used only when a sequence is finite. This also explains why the word "sequence" is mostly seen in mathematics and "list" in computer science.

On the TI-83/84 both words mean the same thing, because we
do not have infinite sequences on a calculator. Operations on lists (under both
names) are in menu 2^{nd} LIST.

Here we give some examples of the use of operations on
sequences, and we strongly recommend that students create their own examples. **The ability to read calculator operations in
plain English is an important step toward understanding them**.

Seq(N^{2},N,1,5) ENTER {1 4 16 25}

A sequence of N^{2}, for N
changing from 1 to 5.

Seq(N^{2},N,1,11,3) ENTER
{1 16 49 100}

A sequence of N^{2}, for N
changing from 1 to 4 to 7 to 10.

Seq(N^{2},N,0,5)→ L1 ENTER {0 1 4 9 16 25}

Store the sequence of N^{2}, when N is changing from
0 to 5, in variable L1.

Variables L1, ... , L_{6} are called list-variables and are used to
store sequences.

Seq(N^{2},N,1,4)={1,4,6,16} ENTER {1 1 0 1}

The = is under TEST. It yields 1 when the equality is true, and 0 when it is false.

Is the sequence of squares of N, for N changing from 1 to 4,
equal to the sequence 1, 4, 6, 16? The first, second and fourth terms are
equal, but the third terms are different. (N^{2} = 9, not 6.)

You can perform all arithmetic operations on sequences, providing that all sequences involved have the same length. You can also mix numbers and sequences. Each number will act on all terms of the sequence. Study the following examples.

√({1,4,9})+1 ENTER. {2 3 4}

Ans/2 ENTER {1 1.5 2}

Ans+{2,-.5,0} ENTER {3 1 2}

The dimension of a sequence is its length.

L1 ENTER {0 1 4 9 16 25}

dim(L1) ENTER 6

The length of the sequence (or list) L1. The length of list L1 is 6.

sum is under LIST MATH.

sum(L1) ENTER 55

The sum of all terms of the sequence L1.

Study the following examples.

{1,1,2,3,5}→L2 ENTER {1 1 2 3 5}

cumSum(L2) ENTER {1 2 4 7 12}

The cumulative sum of L2_{,} or the series L2. A sequence whose n-th term is the sum of the first n terms of L2.

ΔList(L2) ENTER {0 1 1 2}

The sequence of differences of consecutive terms of L2. Its length is always smaller by 1 than the length of L2.

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