Download - Arithmetic Progression
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