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?
Book mark this page in Del.icio.us, Furl, Digg, StumbleUpon, whatever...
Didn't find what you are looking for? Try search:
Need a break? Play a math game. Well, they all involve math... No, really!







