Sequences and Functions

Question 1

What is a sequence?

Answer 1

A Sequence is a list of things (usually numbers) that are in order.

Question 2

What are finite and infinite sequences?

Answer 2

The sequence of odd numbers is infinites

1, 3, 5, 7, …

The sequence of two digit multiples of 3 is finite as sequence stops at 99

Question 3

What is an Arithmetic Sequence?

Answer 3

In an Arithmetic Sequence the difference between one term and the next is a constant.

In other words, we just add some value each time … on to infinity.

Example:

1, 4, 7, 10, 13, 16, 19, 22, 25, …

This sequence has a difference of 3 between each number.
Its Rule is xn = 3n-2

In General we can write an arithmetic sequence like this:

{a, a+d, a+2d, a+3d, … }

where:

a is the first term, and

d is the difference between the terms (called the “common difference”)

And we can make the rule:

xn = a + d(n-1)

(We use “n-1” because d is not used in the 1st term).