 Hello and welcome to the session. In this session we discuss the following question that says, find the 20th term of the HP 1, 1 upon 4, 1 upon 7, 1 upon 10 and so on. Before we move on to the solution, let's discuss when a sequence say A, B, C and so on is a harmonic progression that is HP. This sequence is a harmonic progression when the reciprocal of the terms of the sequence that is 1 upon A, 1 upon B, 1 upon C and so on form arithmetic progression that is AP. The nth term is given by A plus n minus 1 will into B where A is the common difference with the key idea that we use for this question. Let's now move on to the solution. In the question we are given a harmonic progression and we are supposed to find its 20th term. We have 1, 1 upon 4, 1 upon 7, 1 upon 10 and so on harmonic progression. This means that the reciprocal of the terms of this harmonic progression would form an automatic progression so 1, so 7, 10 and so on automatic progression that is AP. The first term is equal to 1 and the common difference which would be B is equal to 4 minus 1 that is 3 and 7 minus 1 is also 3 and 10 minus 7 is also 3. This means 3 would be the common difference. Now since we are supposed to find the 20th term of the HP so for this we can first find the 20th term of this AP. The AP is equal to 4 into D that is 1 plus 20 minus 1 the whole into D which is 3 so this is equal to 1 plus 19 into 3 which is equal to 1 plus T7 and this is equal to 58 so hence we have 1, 4, 7 is equal to 58 HP 1, 1 upon 4 would be the reciprocal of 58 which is 1 upon 58 that is the given HP is 1 upon 58. So 1 upon 58 final answer. Hope you have understood the solution of this question.