how to simply understand the arithmetic progression

2. ASWATHI PV
Msc. Mathematics

3. Introduction
You must have observed that in nature many things
follow a certain pattern, such as the petals of sun
flower , the holes of a honeybee comb, the grains on
maize cob etc. We now look for some patterns which
occur in our daily life.

4. Example-1
Azad applied for a job and got selected. He has been
offered a job with a starting monthly salary 20,000
with an annual increment of Rs. 1000 in his salary. His
salary for the 1st , 2nd ,3rd… Years will be respectively
20000 , 21000, 22000 ….
Here we observe a pattern we find that the
succeeding terms are obtained by adding a fixed
number 1000.

5. Example -2

6. Consider the following lists of numbers
1. 4, 5, 6, 7,……
2. 100, 80, 60,…..
3. -10, -12, -14,……
each of the numbers in the list is called a term

7. In the above list that is in
1. Each term is one more than the term preceding it
2. Each term is 20 less than the term preceding it
3. Each term is -2 more than the term preceding it

8.  In all the lists above, we see that the successive
terms are obtained by adding a fixed number to the
preceding terms. Such lists are called Arithmetic
progression (AP)
 So an AP is a list of numbers in which each term is
obtained by adding a fixed number to the preceding
term except the first term.

9.  This fixed number is called the common difference of
the AP.
 Remember that it can be positive (+) , negative (-) or
zero

10. ?
Check that given terms is in AP or not.
2, 6,10, 14,……
Here the first term = 2
Find the differences in the next terms
2nd term – 1st term= 6 – 2 = 4
3rd term – 2nd term = 10 – 6 = 4
4th term – 3rd term = 14 – 10 = 4
Since the differences are common hence the given terms
are in AP

11. Let us denote the 1st term of an AP by ‘a’, nth term by An,
common difference by d
Then the general form of an AP is
a, a+d, a+2d, ……, a+(n-1) d
nth term of an AP is
An = a + (n-1)d

12. example
Find the 20th term of the AP
7, 10, 13,16,…….
a= 7 , d=3, n=20
A20 = a+19d
= 7 + 19 x 3 = 64

13. ?
1. Find 100th term of AP
2, 4, 6,8………….
2. Find 25th term of AP
9,12,15,…….