 Hello and welcome to the session. In this session we will learn about the arithmetic progression. Consider a list of numbers 1, 2, 3, 4 and so on. In this list of numbers as you can see that each term is one more than the term preceding it that is the successive terms are obtained by adding a fixed number to the preceding terms as in this case the successive term 2 is obtained by adding a fixed number 1 to the preceding term 1 of the list. Such list of numbers is said to form an arithmetic progression. Now the general definition for arithmetic progression is given as that arithmetic progression 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. Consider a, a plus D, a plus 2D, a plus 3D and so on. This represents an arithmetic progression where we have a is the first term and D is the common difference. This is the general form of an AP that is arithmetic progression. Consider the AP 2, 4, 6, 8, 10 and so on in this the first term that is A is 2. The common difference that is D is 2. If in AP that is an arithmetic progression we have finite number of terms then that AP is finite AP that is finite arithmetic progression and if we have infinite number of terms in an AP then that is called an infinite AP. That is in infinite APs we don't have the last term. Consider this AP in this we do not have any last term this is an infinite AP that is we have infinite number of terms in this AP and if you consider this AP this has finite number of terms so this is a finite AP. Now consider a list of numbers a 1, a 2, a 3 and so on. If the difference a k plus 1 minus a k is same for different values of k the list of numbers that we had taken would be an AP that is an arithmetic progression. We have taken this list of numbers in which we have a 1 as this a 2, a 3, a 4 and a 5. Now a 2 minus a 1 is equal to this then a 3 minus a 2 is equal to this then a 4 minus a 3 is equal to this a 5 minus a 4 is also equal to this. So as you can see a k plus 1 minus a k is equal to 4 when we have k equal to 1, 2, 3, 4. Thus this list of numbers that we had taken is an AP that is an arithmetic progression. Now we shall discuss about the nth term of an AP. Consider a general form of the AP a a plus d, a plus 2d, a plus 3d and so on in this the first term is a and the common difference is d. nth term of this AP is given by an equal to a plus n minus 1 into d. This an that is the nth term of the AP is also called the general term of the AP. If we have m terms in an AP then the last term is given by a m also sometimes it is given by the letter L. Consider the AP here the first term a is given by this and the common difference d is this. Let's find out the sixth term of this AP that is we have to find out a 6 which is given by a plus n minus 1 into d that is this. So the sixth term is given by this. Now we shall discuss about the sum of first n terms of an AP. Let the sum of first n terms of an AP be denoted by the letter s. This is equal to n upon 2 multiplied by 2 a plus n minus 1 into d where a is the first term and d is the common difference. This can also be written as s is equal to n upon 2 multiplied by a plus an where this an is the nth term of the AP. If there are only n terms in an AP then an is equal to L that is the last term of the AP then the sum that is s would be given by n upon 2 multiplied by a plus L. Consider this AP where the first term is given by this and the common difference d is given by this. Now we are supposed to find the sum of first 8 terms then we take n equal to 8. Now the sum s is given by n upon 2 multiplied by 2 a plus n minus 1 into d. This is the sum of first n terms of this AP. This completes the session. Hope you have understood the concept of arithmetic progression how we find the nth term of an AP and how do we find the sum of first n terms of an AP.