Arithmetic progression





In this page arithmetic progression we are going to see,what is mean by A.P? .Its general form. Meaning of each letter in that form some example problems with detailed steps.

Consider the following patterns:

(i)   2,6,10,14,18,22,............

(ii)  5,10,15,20,25,..............

(iii)  -9,-5,-1,3,7,..............

In these sequence each term after the first term differs from the previous term by a constant. The constant is same in the whole sequence.From the first sequence

The difference 4 is common for the whole sequence. These types of sequences are called as Arithmetic sequences.

progression:

Sequences following certain pattern are known as progression.Each Patterns follows a particular rule.All the progressions are called sequence. But all the sequence is not a progression.

Definition of Arithmetic progression:

A sequence is said to be an a.p if the difference of each term,except the first one,from its preceding is always same.

General form of A.P

 a, (a+ d),(a+2d),(a+3d),.........................

Here a = first term

       d = common difference

we have formula to find common difference

d = t2 - t1
nth term of A.P

tn = a + (n-1)d

Example 1:

The first term of an A.P is 6 and the common difference is 5.Find the A.P and its general term.

Solution:

The first term a = 6

the common difference = 5

To find the A.P we need at least first three terms of the sequence.

General form of A.P is a,(a+d),(a+2d),...................

6,(6+5),(6+2(5)),..................

The sequence A.P is 6,11,16,...............

General term:

tn = a + (n-1)d
tn = 6 + (n-1)5

    = 6 + 5n - 5

    = 6 - 5 + 5n  

tn = 1 + 5n

Example 2:

The fifth term of an A.P is 27 and the eight term is 12.Determine the first term and the common difference.

Solution:

Fifth term = 27

eight term = 12

t5 = 27
t8 = 12

a+ 4d = 27 -----------(1)

a+7d = 12 -----------(2)

(2)-(1) d = -5

Substitute d= -5 in (1) equation we get

a + 4(-5) = 27

a -20 = 27

      a = 27 + 20

      a = 47

Therefore the first term = 47 and the common difference = -5

Related Topics

Quote on Mathematics  arithmetic progression

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

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