 Hello and welcome to the session. In this session we will discuss a question which says that given the explicit formula of a geometric sequence, find the first 5 terms of the sequence and the explicit formula is given as a m is equal to 2 into 1 by 4 always to power n minus 1. Now before starting the solution of this question, we should know some results. First is the formula for the geometric sequence is given by a m is equal to a 1 into r is to power n minus 1 is equal to 1 in German and even r square even r cube and so on into r is to power n minus 1 and so on. There r is second term and continuing like this, minus 1 is the n-th term of the geometric sequence. Now these results will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now in this question, we are given the explicit formula for the geometric sequence and we want to find the first 5 terms of the sequence n is equal to into 1 by 4 whole raise to power n minus 1. Now using the result which is given to us in the key idea formula for the geometric sequence is given by n is equal to a 1 into r 1 where n is greater than equal to 1 comparing this with the given s 1 upon 4. Now from the key idea we also even r even r square minus 1 and so on. First term even r is the second term and continuing like this minus 1 is n-th term of the geometric sequence. So first 5 terms of the sequence are even then even r then even r square then even r cube and even r 4 already obtained even is equal to 2 and r is equal to 1 upon 4 r in this sequence that is 2 that is 2 into 1 upon 1 upon 4 whole square that is 2 into 1 upon 4 whole cube even into r is into 1 upon 4 whole raise to power 4 1 upon 2 upon 4 whole square into 1 upon 16 that is equal to 1 upon 4 whole cube is equal to 2 into 1 upon 64 that is equal to 1 upon 32 now first term is 2 into 1 upon 4 equal to 2 into 1 upon 2 1 upon 8 and upon 32 upon 128 hope you all have enjoyed the session.