 Hi and welcome to the session. I'm Kanika and I'm going to help you to solve the following question. The question says find that 12th term of a geometric progression whose 8th term is 192 and the common ratio is 2. Now before solving this question we should know that geometric progression is of the form a a r a r square a r q and so on. The general term of this progression is given by d n is equal to a into r to the power n minus 1 where a is the first term of the progression r is the common ratio which is obtained by dividing any term by its preceding term or we can say that r is obtained by dividing nth term by n minus 1th term. Let's now begin with this illusion. Now in this question we have to find that 12th term of a GP whose 8th term and common ratio is given to us. Now let a be the first term with the common ratio of a GP. Now the 8th term that is t 8 is equal to a into r to the power 8 minus 1 and this is equal to a into r to the power 7. In the question we are given that 8th term is equal to 192 so we have t 8 is equal to a into r to the power 7 is equal to 192. Let's name this equation as equation number 1. Now the 12th term that is t 12 is equal to a into r to the power 12 minus 1 and this is equal to a into r to the power 11. Now a into r to the power 11 can be written as a into r to the power 7 into r to the power 4 from 1. We know that a into r to the power 7 is equal to 192 and in the question we are given that common ratio that is r is equal to 2. Now substitute the value of a into r to the power 7 and r in this expression. By substituting the values we get 192 into 2 to the power 4 and this is equal to 192 into 16 and this is equal to 3072. Hence the 12th term of a GP that is t 12 is equal to 3072. Hence our required answer is 3072. This completes the session by NJKL.