 So here is another question folks. Determine the 10th term from the end of the AP 4 9 14 254 Okay, so what do we need to find out? e 10th term from the end. So we don't know what is you know, so 10th term from the end 10th term from the end So there are two ways of doing it. Either you know what is the 10th term from the end? so that will be a longer method maybe and You do it from the end itself. So hence we know the formula nth term nth term from end is simply e last last term minus n minus 1 times d where d is common difference D is we had derived this in the theory portion, right? D is common difference common Difference, so the formula is t last last term minus n minus 1 times d. What is last term 254? What is n 10 minus 1 into d? D is in this case is if you see 9 minus 4 is the consecutive term differences D so what is the d value 5, right? So it is nothing but 254 minus 9 times 5 which is 254 minus 45 which is 2 0 9 right, so this will be the 10th term From last you could have solved this In different way in one more method. How? So 10th term from the end So if you see first of all find out how many terms are there? So n let's find out total number of terms in the sequence number of terms number of terms Is equal to what right so number of terms how to find out? Let's say 254 is the last term T1 is 4 plus. Let's say m is the number of terms in the AP so m minus 1 into 5 Okay, last term is in first term plus m minus 1 times d. This is what so this is 250 divided by 5 is m minus 1 correct so 50 is equal to m minus 1 So m is equal to 51. So there are 51 terms in the in the given sequence correct now first term from the end is the last term correct first term from and Is e 51 First term from the big last term law first term from end is the last term from beginning right now second term from and Will be t 51 minus 1 that is t 50 Okay, so you just note here when this is second here. It is one Okay, so third term similarly third term from and is e 51 minus 2 this is the trend. I'm not going to write down all those till 10 terms So you quickly can observe that 10th term 10th term from and will be simply t 51 minus 9 right one less than whatever is appearing here, correct now. So which is nothing but e 42 So the 42nd term from the beginning is the 10th term from the end. So can't we find out e 42? Yes, we can e 42 is t 1 plus 41 or let me write like that 42 minus 1 n minus 1 that is into d 5 Let's deploy the values e 1 was how much e 1 was 4 and Then it is 41 into 5. So if you see this is 4 plus 205 which is 209 So both ways you can find out the nth term from the end. Okay, so there are two ways of finding or solving this particular problem