Introduction to Arithmetic Progression






Notes:

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

You must have observed that in nature, many things follow a certain pattern, such as the petals of a sunflower.

Consider the following lists of numbers:
(i) 1, 2, 3, 4, . . .
(ii) 0, 10, 20, 30, 40, . . .
(iii) –5, –4, –3, –2, –1, 0, 1, 2, . . .
(iv) 5, 5, 5, 5, . . .
(v) 4, 2, 0, –2, –4, –6 …
Each of the numbers in the list is called a term.

Let see what pattern they are having.
In (i), each term is 1 more than the term preceding it.
In (ii), each term is 10 more than the term preceding it.
In (iii), each term is obtained by adding –1 (subtracting 1) to the term preceding it.
In (iv), all the terms in the list are 5, i.e., each term is obtained by adding (or subtracting) 0 to the term preceding it.
In (v), each term is obtained by adding – 2 to (i.e., subtracting 2 from) the term preceding it.

In all the lists above, we see that successive terms are obtained by adding a fixed number to the preceding terms. Such list of numbers is said to form an Arithmetic Progression ( AP ).

So, an arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

This fixed number is called the common difference of the AP. Remember that it can be positive, negative or zero.

Consider the list of numbers
1, 1, 2, 3, 5, . . . .
By looking at it, you can tell that the difference between any two consecutive terms is not the same. So, this is not an AP.



   


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