 Hi and welcome to the session. I am Kanika and I am going to help you to solve the following question. The question says find the 20th and in it terms of the geometric progression 5 by 2, 5 by 4, 5 by 8 and so on. Before solving this question we should know that geometric progression is of the form a, a r, a r square, a r cube and so on. The general term of this progression is given by Tn is equal to a into r to the power n minus 1 where a is the first term, r is the common ratio which is obtained by dividing any term by its preceding term. But we can say that r is obtained by dividing any nth term by n minus 1th term. Let's now begin with the solution. Given geometric progression is 5 by 2, 5 by 4, 5 by 8 and so on. We have to find the 20th and the nth term. So let's first find the 20th term. Now here a that is first term is equal to 5 by 2. Let's now find r. We know that r is obtained by dividing any term by its preceding term. So r is equal to 5 by 4 divided by 5 by 2. And this is equal to 5 by 4 into 2 by 5 and this is equal to 1 by 2. Since we need to find the 20th term, therefore we will substitute n as 20 in the general term of the geometric progression which is tn is equal to a into r to the power n minus 1. By substituting n as 20 in the general term, we get t20 is equal to 5 by 2 into 1 by 2 raised to the power 20 minus 1. And this is equal to 5 by 2 into 1 by 2 raised to the power 90. Now this can be written as 5 by 2 to the power 1 into 1 by 2 to the power 90. And this is equal to 5 by 2 to the power 20 by the law of exponents. Now we will find the nth term. We know that tn is equal to a into r to the power n minus 1. Now here a is equal to 5 by 2 and r is equal to 1 by 2. So we have 1 by 2 to the power n minus 1 and this is equal to 5 by 2 into 1 by 2 to the power n minus 1. And this is equal to 5 by 2 to the power n. Hence the 20th term is 5 by 2 to the power 20 and nth term is 5 to the power 2 to the power. This is a required answer. So this completes the session. Bye and take care.