- Introduction
- |
- What is arithmetic progression
- |
- Some Important points about AP
- |
- nth term of Arithmetic Progression
- |
- Sum of nth item in Arithmetic Progression

So here we see the pattern in Rohan salary. The difference between two consecutive year salaries is constant. In the similar, world around us present us these pattern in many form. In this chapter, we will learn a special type of pattern called Arithmetic Progression

Let us consider following series

All these sets follow certain rules. In first set 5 - 1 = 9 - 5 = 13 - 9 = 17 - 13 = 4

In second set 2 - 1 = 3 - 2 = 4 - 3 = 1

and so on.

Here the difference between any successive members is a constant

Such series are called Arithmetic Progression

- The difference is called the common difference of the AP and It is denoted by d
- The members are called terms. The first member is called first term
- We can denote common difference by d
- If a
_{1}, a_{2},a_{3},a_{4},a_{5}are the terms in AP then

D=a_{2 }-a_{1}=a_{3}- a_{2}=a_{4}– a_{3}=a_{5}–a_{4} - We can represent the general form of AP in the form

a,a+d,a+2d,a+3d,a+4d………..

Where a is first term and d is the common difference - If the AP series has last term then it s finite Arithmetic Progression and if the AP series has infinite then it is called the Inifinite Arithmetic Progression

1, 4, 7, 10, 13, 16, 19, 22, 25, ...

D=3=3=3=3

So it is AP

a, a + d, a + 2d, a + 3d, .........................

Here a = 1, d = 4

a + d = 1 + 4 = 5

a + 2d = 1 + 2 x 4 = 9

and so on

Thus we can say that

a = First term

a + d = Second term

a + 2d = Third term

a + 3d = Fourth term and son on

n

Here First term = t

Second term = t

and hence, t

d is called common difference and the series is called arithmetic progression

S = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

Adding these two we get 2s = 11 + 11 + 11 + 11 + 11 + 11 + 11 = 11 + 11 + 11

= 10 X 11

s = (10 X 11)/2 = 55

In similar way, if

Adding we get

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