 product of first three terms of the gp is 10000 so you can find out no there could be any number any number of terms if 6 is added to its second term and 7 is added to its third term then the terms become in AP that means the first three terms become in AP find the GP product of first three terms of GP 1000 again what do you need to you have to take into R sorry into a into a R these are the three terms in GP always and their product is 1000 so what is a what is the value of a a is equal to 10 right so the second term is 10 okay now it is said that if 6 is added to second term so what will be the second term now 6 is added so 16 will be the second term right now a by R and they are saying a and a are these were originally in GP so 10 upon R 10 and 10 R are in GP now they're saying add 6 to the second term so 10 plus 6 16 and add 7 to the third term so 10 R plus 7 along with the first term they are now in AP they are in AP so what is the criteria for AP consecutive terms will have common difference same so 16 minus 10 upon R must be equal to 10 R plus 7 minus 16 is it it yes so hence what will you get you will get 10 R plus 10 upon R and here 7 minus 16 is minus 9 minus 25 this is the equation right multiply by our whole equation you will get 10 minus 25 R is equal to 0 and divide by 5 you will get 2 R square plus 2 minus 5 R is 0 yes mean of this thing or same thing this is where the mean comes from so B minus a is equal to C minus B then 2 B is equal to a plus C or B is a plus C by 2 right it's same thing now so when you do this correct solve this quadratic it is 2 R square again minus 5 R can be written as minus 4 R minus R plus 2 is equal to 0 right so this is 2 R R minus 2 minus 1 R minus 2 is 0 so R minus 2 and 2 R minus 1 is 0 so that means R is equal to 2 or R is equal to half right so 2 and so now let's find out a is 10 and R is 2 in that case it is 5 10 and 20 and if a is 10 and R is half then it is 20 10 5 so these are the two deep