13.1 Sequences

Definition of a Sequence 2, 5, 8, 11, 14, …, 3n-1, … A sequence is a list. A sequence is a function whose domain is the set of natural numbers. In mathematics, natural numbers are the ordinary counting numbers 1, 2, 3,... (sometimes zero is also included). The values of this function are called terms. Sometimes a sequence is called a progression. The notation is used to denote the sequence.

Find the next term in each sequence below. #11,3,7,11,13,… #2230,460,46,92,9.2,… #33,12,24,33,66,…

Example Write the first three terms of the sequence where. All sequences have an infinite number of terms. In some cases, we want to consider only a finite number of terms. An array is a function whose domain is a finite subset of the natural numbers.

Example Write the array consisting of the first six terms of the sequence.

Sequences of Partial Sums also known as “finite series” Math or engineering fields Computer science Vectors in HPC A partial sum is the total of the terms of a sequence up to a given term.

Associated with every sequence is another sequence called the sequence of partial sums. Example List the first five terms of the sequence. Find the first 4 terms of the sequence of partial sums.

Find the 4 th term. #15,25,125,…,,… #2 #3

List the first six terms. #1 #2 #3

Give the fourth through eighth terms of each sequence. #1 #2

List the first five terms of the sequence. Find the first 4 terms of the sequence of partial sums.