What is x if x+1, x-1, 4 are terms of an arithmetic series?

To determine the terms of the given arithmetical
progression, we'll have to find out the value of x,
first.

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

x - 1 = [(x+1) +
4]/2

We'll multiply by 2 both
sides:

2x - 2 = x + 1 +
4

We'll combine like terms from the right
side:

2x - 2 = x + 5

We'll
subtract x+5:

2x - 2 - x - 5 =
0

x - 7 = 0

We'll add 7 both
sides:

x =
7

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