 Hello and welcome to the session I am Deepika and I am going to help you to solve the following question the question says Which term of the AP? 3, 15, 27, 39 so on will be 132 more than its 54th term Now we know that the unit term a n of the AP with first term a and common difference d is given by a n is equal to a plus n minus 1 into d So this is the key idea behind that question We will take the help of this key idea to solve the above question So let's start the solution The given AP is 15, 27, 39 so on Now according to our key idea a is the first term of the AP so here the first term is 3 So here a is equal to 3 and d is the common difference So here d is equal to 15 minus 3 which is equal to 12 Now according to the given question we have to find the term of the AP which will be 132 more than its 54th term So let us first find out which is the 54th term Now according to our key idea we have a n is equal to a plus n minus 1 into d So a 54 is equal to 3 plus 54 minus 1 into 12 and this is again equal to 3 plus 53 into 12 and this is equal to 3 plus 636 Therefore a 54 that is the 54th term of the given AP is 639 Now let kth term of the given AP is 132 more than its 54th term that is a k is equal to 639 plus 132 which is again equal to 771 So this implies a which is 3 plus k minus 1 into d that is 12 is equal to 771 This implies 12 into k minus 1 is equal to 771 minus 3 This implies k minus 1 is equal to 768 over 12 and this is equal to 64 This implies k is equal to 64 plus 1 which is equal to 65 Hence 65th term of the given AP will be 132 more than its 54th term So this is the answer for the above question This completes our session I hope the solution is clear to you Bye and have a nice day