in geometric prograssion the difference between 7th and 5th terms is 192 and the difference between 15th and 3rd terms is 48. find the common ratio
the difference between 7th and 5th terms is 192
---> ar^6 - ar^4 = 192
ar^4(r^2 - 1) = 192 **
the difference between 15th and 3rd terms is 48
---> ar^14 - ar^2 = 48
ar^2(r^12 - 1) = 48 ***
divide ** by ***
r^2(r^2 - 1)/(r^12 - 1) = 4 ****
r^4 - r^2 = 4r^12 - 4
4r^12 - r^4 + r^2 - 4 = 0
clearly, by inspection, r = ±1 would be a solution to this last equation , but not in ** or ***
Something is awry here, did you really mean "difference" ?