You must have observed that in nature, many things follow a certain pattern, such as the petals of a sunflower, the holes of a honeycomb, the grains on a maize cob, the spirals on a pineapple and on a pine cone etc. We now look for some patterns which occur in our day-to-day life. Some such examples are :

Each of the numbers in the list is called a term.
Given a term, can you write the next term in each of the lists above? If so, how
will you write it? Perhaps by following a pattern or rule. Let us observe and write the
rule.

(1) each term is 1 more than the term preceding it.

(2) each term is 30 less than the term preceding it.

(3) each term is obtained by adding 1 to the term preceding it.

(4) all the terms in the list are 3 , i.e., each term is obtained by adding
(or subtracting) 0 to the term preceding it.

Let us consider the situation again, given in Section 5.1 in which Reena applied for a
job and got selected. She has been offered the job with a starting monthly salary of
Rs 8000, with an annual increment of Rs 500. What would be her monthly salary for
the fifth year?

To answer this, let us first see what her monthly salary for the second year
would be.

Let us consider the situation again given in Section 5.1 in which Shakila put Rs 100 into her daughter’s money box when she was one year old, Rs 150 on her second birthday, Rs 200 on her third birthday and will continue in the same way. How much money will be collected in the money box by the time her daughter is 21 years old?

In this chapter, you have studied the following points :

1. An arithmetic progression (AP) is a list of numbers in which each term is obtained by
adding a fixed number d to the preceding term, except the first term. The fixed number d
is called the common difference.

2.4. The sum of the first n terms of an AP is given by :

3.If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP
is given by :