 Like we had selection of terms in AP, we have selection of terms in GP So if you have the you know if you recall if three terms were given in AP we used to consider a-d a A plus D like that. These are three terms in AP Likewise in GP also if let's say they are giving three terms in GP. So Three terms three terms in GP Right, anyone can guess what could be the three terms in GP GP. Can you tell me what could be the three terms in GP? So what three irrespective of the value of A and R? They will always be in GP So it will be anyone Can think of what will be three terms in GP always anyone No clue So you can take a hint from here If it was a-d a a plus D what will be three terms in GP that a upon R A and a R are always in GP isn't it Why is the common ratio guys common ratio in this case? R common ratio is Okay, tell me what if you have four terms in GP tell me four terms in GP What are the four terms in GP? In AP what used to happen in AP if you see we used to have a-3d a-d Then a plus D and then a plus 3d. So here. What do you think should be four terms? Yeah, that's in AP what what about here? Since you see a by R cube Then a upon R Then a R Then a R cube. What is the common ratio? Common ratio in this case. What is the common ratio? R square very good Very good third one five terms in AP this will be very simple Now you could sorry five terms in GP now you know the pattern So what will be the five terms in it GP? Yes, perfect so a upon R square a upon R a A R Yeah, what is the common ratio common ratio in this case is R right? So whenever you have to select terms in GP three four five times whatever you now know Let me solve this sum of three terms in GP. So, you know if you have to select three terms in GP what all? A by R Plus a plus a R is 38 first equation and Product is 1728 so a by R and exactly this reason why we took this kind of These terms right because the product may it helps 1728. So this R and this R goes so a cube is 1728 Which is 12 cube so clearly a is equal to 12 right? So a is 12 when a is 12 then You can find out From the first equation you can write 12 upon R Plus 12 plus 12 R is 38 right so you can cancel to so this is 6 6 6 19 So and then multiply the entire equation by R. What will you get? 6 plus 6 R Plus 6 R square is 19 Right, so 6 R square My 19 R 19 R minus 6 R is Minus 13 R and Then plus 6 is 0 So 6 R square Minus 9 R minus 4 R Plus 6 is 0. So this becomes 3 R common 2 R minus 3 Minus 2 common 2 R minus 3 is 0 So 2 R minus 3 3 R minus 2 is 0 So you get R is equal to 3 by 2 see again an exercise on quadratic equation Correct for two values of R is there and one a was now what are Terms a by R a and a R So an R is 3 by 2 So this will be 12 by 3 into 2 Then 12 and 12 into 3 by 2 Which means 8 12 and 18 Just Never so 8 12 and 18 right and if R is 2 by 3 Then it is 12 into 3 by 2 12 12 into 2 by 3 correct. So 18 12 And it