Three numbers are in A.P. and their sum is 15. If 1, 4 and 19 are added to these numbers respectively, the resulting numbers are in G.P. Find the numbers.

The nth term of a G.P. is 128 and the sum of its n terms is 255. If its common ratio is 2, then find its first term.

How many terms of the G.P. 3, 3², 3³, …. are needed to give the sum 120?