 Hello and welcome to the session let's work out the following problem it says which term of the arithmetic progression 3, 10, 17 so on will be 84 more than its 13th term. So let's now move on to the solution we have to find the term of the arithmetic progression which is 84 more than its 13th term. So let the nth term of the arithmetic progression is 84 more than its 13th term and its term is 84 more than its 13th term so nth term would be the 13th term plus 84 since it is 84 more than its 13th term. Now also nth term of an AP is given by the formula A plus n minus 1 into D where A is the first term and here A in this arithmetic progression is 3 and D is the common difference which is equal to 7 since 10 minus 3 is 7, 17 minus 10 is 7 so using this we have nth term A n is equal to 13th term that is A 13 plus 84 so now we find A 13 using this formula now A is 3 plus n minus 1 into D n is 13 here 13 minus 1 into 7 plus 84 so this is equal to 3 plus 12 into 7 plus 84 and this is equal to 171 now we have to find the value of this n that is we have to find which term is this now we know that A n is given by A plus n minus 1 into D and we know that nth term is 177 now A is 3 plus n minus 1 into 7 is equal to 171 so this implies n minus 1 into 7 is equal to 171 minus 3 so this implies n minus 1 into 7 is equal to 168 so this implies n minus 1 is equal to 168 divided by 7 and this implies n is equal to 168 divided by 7 plus 1 so we have 168 plus 7 divided by 7 so this is equal to 175 divided by 7 so this implies n is equal to 25 so 25th term of this AP is 84 more than its 13th term so 25th term is the answer so this completes the question and the session bye for now take care have a good day