Trick Math Problem. Cant find it out?

Question

The number 17 is the first number in a sequence in which 77 is the 17th number. Each of the numbers beyond the first two in the sequence is the mean of all previous numbers.

What is the second number in the sequence?

Thanks

Answer 1

It's really easy.  If you just make it so the first two numbers average to 77, then all the subsequent numbers will be 77.

17

137

77

77

77

77

77

77

77

77

77

77

77

77

77

77

77

etc.

Answer:

137

Answer 2

In order for each sequence member to be the mean of its two predecessors, the sequence must be arithmetic, i.e. there is a constant difference between terms.  There are 16 terms to go from 17 to 77, so the constant difference is 60/16 = 3.750.  Hence, the second number is 17 + 3.750 = 20.750.  However, since the problem poses no constraints on the first two numbers, the second answer above is also correct, and there are an infinity of other valid solutions.

Answer 3

never mind, that's wrong, so was my second thought... need to think about it some more.

Puzzle is right, I was making it too hard.