Insert 4 arithmetic means between 3 and 23

Insert 6 arithmetic means between 3 and 24.

Insert 3 arithmetic means between : 3 and 15.

Insert 5 arithmetic means between 8 and 26.

Insert 3 arithmetic means between : 5 and 21.

Insert 10 arithmetic means between 2 and 57.

Insert 4 geometric means between 6 and 192.

There are n arithmetic means between 3 and 17. The ratio of the last mean to the first mean is 3: 1. Find the value of n.

Insert 6 harmonic means between 3 and (6)/(23)

Let A_(1),A_(2),A_(3),"......."A_(m) be arithmetic means between -3 and 828 and G_(1),G_(2),G_(3),"......."G_(n) be geometric means between 1 and 2187. Product of geometric means is 3^(35) and sum of arithmetic means is 14025. The value of n is

Let A_(1),A_(2),A_(3),"......."A_(m) be arithmetic means between -3 and 828 and G_(1),G_(2),G_(3),"......."G_(n) be geometric means between 1 and 2187. Product of geometric means is 3^(35) and sum of arithmetic means is 14025. The value of m is