 welcome friends and we are going to take up one example problem to see and understand whatever we learned in the previous session so the question says find the hundredth term of the following sequence and the sequence is 7 12 17 22 27 and let's say we do not have any idea of what kind of sequence it is and whether it is arithmetic progression or whatever let's say we don't have any clue then in the previous session if you remember we discussed that if the subsequent or let's say two consecutive terms in a sequence have same common difference same difference that is then we know how to deal with such cases so let's say the difference here is if you clearly see is five and five right the first layer of difference between two consecutive term is always five in such cases we said that the nth term of our sequence can be given as tn as an plus b right it can be expressed as a linear function of n where n is what the position number or and the term number right so n is one two three four like that correct this is what we learned in the previous session so we are going to use this particular concept to find out the nth term in this case or here it has been given to find out hundredth term so for that if I somehow get this relationship then if I deploy n is equal to 100 I will get the hundredth term so let's see how to go about it so the underlying concept once again just to reemphasize if you have a sequence and the consecutive terms have constant difference to consecutive term has the same difference for the entire sequence then any term any term of that sequence can be expressed like this tn is equal to an plus b where a and b are constants n is the term number correct so if you see clearly here t1 let's say n is equal to 1 if you put n is equal to 1 t1 is how much a into 1 plus b that is a plus b correct t1 will be this much but in the given sequence t1 is 7 first term is 7 so can't I say that a plus b is equal to 7 right a plus b is 7 now what about t2 that is n is equal to 2 if you check it will be t2 second term and if you put in the relationship n is equal to 2 you will get a2 plus b which is 2 a plus b and if you see the value of the second term from the given sequence is 12 so can I not just deploy 12 here okay so now from our knowledge of linear equations we can solve these two equations and find the value of a and b so let's say this equation is 1 and this equation is 2 so 2 minus 1 if I do then what will happen you'll get simply a equals 5 12 minus 7 is 5 right so a is equal to 5 if you do this you will get a is equal to 5 and if a is equal to 5 clearly from 1 from 1 if you see b will be simply 7 minus a 7 minus a is nothing but 7 minus 5 which is 2 okay so hence I get the nth term t and relationship as a n so a was 5 so 5n plus 2 right this is the relationship generic relationship for any given term okay nth term so now what was the question to question was to find out hundredth hundredth term so how to find hundredth term in this case so this will be simply t100 that means n is equal to 100 so put n equals 200 and simply add 2 right so hence it is nothing but 502 is the hundredth number in this sequence right so once again underlying philosophy of this question is you have to see that if the sequence constant if the consecutive terms are having the same difference then the sequence can be written like that or nth term can be written like that a n plus b from the known values of t1 t2 and whatever you find out the values of a and b if you deploy the values of a and b you will get the relationship we got in this case 5n plus 2 and now deploy for any n for example if someone now ask you find out the 200th term so clearly t200 will be nothing but 5 into 200 plus 2 it's like we got a formula to find out any any number in that sequence without actually going through each and every term of that sequence that was the purpose of this problem