Arithmetic Progression

PRESENTED TO: PRESENTED BY:Mrs. Rashmi Sharma ISHITA MALIK CLASS : XTH –B ROLL NO: 21

Definition

Arithmetic Progression (also called arithmetic sequence), is a sequence of numbers such that the difference between any two consecutive terms is constant. Each term therefore in an arithmetic progression will increase or decrease at a constant value called the common difference, d.

Examples of arithmetic progression are:• 2, 5, 8, 11,... common difference = 3• 23, 19, 15, 11,... common difference = -4

INTRODUCTION

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2.

INTIAL TERM• If the initial term of an arithmetic progression is a1 and the

common difference of successive members is d, then the nth term of the sequence is given by:

We want a sequence of numbers. Let's start with a number: a1.Now add a number d, (for "difference"). We get a1 + d and the first 2 terms in our sequence are: a1, a1 + d For the next term, let's add d to that last term and

we have a1 + 2d.Our sequence is now: a1, a1 + d, a1 + 2d We continue this process for as long as

we can stay awake. The resulting set of numbers is called an arithmetic progression (AP) or arithmetic sequence.

EXAMPLE

• Let's start with a1 = 4 and then add d = 3 each time to get each new number in the sequence. We get:

an = a1 + (n -1)d

• 4, 7, 10, 13, … The nth term, an of an AP is:

Derivation of Formulas...

SUM

The sum to terms of an AP is:

                

THANKS