Introduction

Introduction to Arithmetic Progression

Think of a group of numbers where the gap between one number and the next one is always the same, like how we count money in 50 naira jumps.

A sequence in which the terms either increase or decrease in equal steps is called an arithmetic progression.

This means the numbers go up or down by the same amount every single time.

Let us look at how we write it with letters.

A sequence a1, a2, a3,…, an,… is called an arithmetic sequence or arithmetic progression if an + 1 = an + d, n ∈ N,

This formula is just saying that if you add a fixed number to the current term, you will get the next term.

The first number in the list and the gap between numbers have special names.

Where a1 is called the first term and the constant term d is called the common difference.

So, the very first number is your starting point, and the 'common difference' is that same amount you keep adding.

Standard form of an A.P.

Let us look at the normal way to write an A.P. using the letter 'a' for the start and 'd' for the gap.

Let us consider an A.P. (in its standard form) with first term a and common difference d

It looks like this when you write it out:

a

a + d

a + 2d

a + 3d

i.e. a, a + d, a + 2d, …

Finding any term in the sequence

If you want to find a number far down the list without writing everything out, use this general formula.

Then the nth term (general term) of the A.P. is

an = a + (n – 1) d

This formula helps you find the value of any position in the sequence easily.