The fifth term of a geometric progression is 16 and the tenth term is 54 .find the first term and common ratio and find the fifteenth term

Answer 1

there are 5 terms between 16 and 54, so r^5 = 54/16 = 27/8
This would have been a lot easier if it had been the 8th term, instead of the 10th, right? Then we'd have had r = 3/2

But now we have r = (3/2)^(3/5)
so a = 16 * r^-4 = 16 * (2/3)^(12/5)
a_15 = a_10 * r^5 = 54 * 27/8 = 729/4