# Given the numbers x+1, 1-x, 4 what is x if the numbers are the consecutive terms of an A.P.

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The terms x + 1, 1 - x and 4 are consecutive terms of an AP. The terms have a common difference.

4 - (1 - x) = d

1 - x - (1 + x) = d

=> 4 - 1 + x = 1 - x - 1 - x

=> 3 + x = -2x

=> 3 = -3x

=> x = -1

**The number x = -1**

If we are given three consecutive terms of an arithmetic progression, the sum of the first and third terms is twice that of the middle term.

x+1, 1-x and 4 terms of an arithmetic progression.

This gives x + 1 + 4 = 2*(1 - x)

x + 5 = 2 - 2x

3x = -3

x = -1

The required value of x is -1.

We'll apply the mean theorem to the consecutive terms of the given artihmetical sequence:

1 - x = (x+1+4)/2

1 - x = (x+5)/2

2 - 2x = x + 5

We'll move all terms to the left:

-2x - x + 2 - 5 = 0

We'll combine like terms:

-3x - 3 = 0

-3x = 3

x = -1

**The requested value for x is: x = -1.**