## Arithmetic Progression

Arithmetic Progression (AP) is the addition of consecutive terms.

Eg. ,

Consecutive means one after the other so there is an equal difference between each term

So, to add on to the example, the AP would be something like this:

,

where is the first term and is the common difference.

The -th term of an AP can be found by:

The formula is quite self-explanatory.

The sum of the first terms of an AP also can be found by applying the formula below:

In order to find the number of terms in an AP, we must apply the formula below:

Example 1

Find the value of .

**Solution 1**

Here I introduced the Sigma Notation. It basically represents the word ‘sum’.

The sum can be written as . In general,

, where and .

So, in the question, it is asking us to find out the sum of . By applying the sum of AP, we get:

.

Random Questions to try out:

1)

2)

More Chim stuff…

Sum of Squares:

Sum of Cubes:

Sun of Triangle numbers:

All the proofs of the properties above requires knowledge of Mathematical Induction (MI) which is really hard to explain so we’ll leave it as such for now. Do go and read up on MI

More random questions:

3) ??? ( SMOPS 2010)

Here is a program for arithmetic progression just for fun.

__Arithmetic Progression__

First Number:

Difference:

Number of Progressions:

Thks,

etzhkysy