1. Arithmetic Progressions
by M. Bourne
We want a sequence of numbers. Let's start with a number: a1.
Now add a number d, (for "difference").
We get a1 + d and the first 2 terms in our sequence are:
a1, a1 + d
For the next term, let's add d to that last term and we have a1 + 2d.
Our sequence is now:
a1, a1 + d, a1 + 2d
We continue this process for as long as we can stay awake. The resulting set of numbers is called an arithmetic progression (AP) or arithmetic sequence.
Example
Let's start with a1 = 4 and then add d = 3 each time to get each new number in the sequence. We get:
4, 7, 10, 13, …
The nth term, an of an AP is:
LiveMath can give us the n-th term of an AP:
Sum of an Arithmetic Progression
The sum to n terms of an AP is:
LiveMath can give us the sum to n terms of an AP.
Example 1
Using the second formula, find the sum of the first 10 terms for the series that we met above: 4, 7, 10, 13, ...
Example 2
Find the sum of the first
1000 odd numbers.
Example 3
A clock strikes the number of times of the hour. How many strikes does it make in one day?
Didn't find what you are looking for on this page? Try search:
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Algebra Lessons on DVD
Easy to understand algebra lessons on DVD. See samples before you commit.
More info: Algebra videos
Book mark this page
Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...
Need a break? Play a math game. Well, they all involve math... No, really!
