Question

Define sequence and give an example.

Short answer

Question: Define what a sequence is and provide an example. Answer: A sequence is an ordered list of elements, in which each element is called a term. The terms in a sequence can be numbers, functions, or other mathematical objects, and can be either finite or infinite. An example of a sequence is the sequence of even numbers: {2, 4, 6, 8, ...}, which can be generated using the formula "a_n = 2n" for n = 1, 2, 3, ....

Step-by-step solution

Define a sequence

A sequence is an ordered list of elements, in which each element is called a term. The terms in a sequence can be numbers, functions, or other mathematical objects. Sequences can be finite or infinite, depending on the number of terms they contain. A sequence is usually denoted as (a_n) or {a_n} for n = 1, 2, 3, ..., where 'n' is the position of each element in the sequence, and 'a_n' represents the element at the nth position.

Provide an example

An example of a sequence would be the sequence of even numbers: {2, 4, 6, 8, ...}. In this sequence, the first term a_1 is 2, the second term a_2 is 4, the third term a_3 is 6, and so on. One could generate the terms of this sequence using a formula, such as "a_n = 2n" for n = 1, 2, 3, .... Using this formula, we can find any term of this sequence by substituting 'n' with the desired position. For example, to find the 5th term of this sequence, we can substitute n = 5 into the formula, and we get a_5 = 2×5 = 10, so the 5th term in this sequence of even numbers is 10.