Find n if (n+1), (n-1), 4 are the terms of n arithmetic sequence.

The terms (n+1), (n-1), 4 are the consecutive terms of
a arithmetical progression (sequence) if and only if the middle term is the arithmetical
mean of the neighbor terms:

n - 1 = [(n+1) +
4]/2

We'll multiply by 2 both
sides:

2n - 2 = n + 1 +
4

We'll combine like terms from the right
side:

2n - 2 = n + 5

We'll
subtract n and add 2 both sides:

n =
7

The terms of the
arithmetical sequence, whose common difference is d = -2 are: 7+1 = 8 , 7-1 = 6 ,
4.