Question

If the numbers x+3,2x+1and x-7are in AP then find x​

Answer 1

x = -3.

Explanation:

As it is an Arithmetic Progression the differences between successive terms are common, so:

2x + 1 - (x + 3) = x - 7 - (2x + 1)

2x - x + 1 - 3 = x - 2x - 7 - 1

x - 2 = -x - 8

2x = -8 + 2 = -6

x = -3.

Answer 2

-3

Explanation:

If these numbers are part of an arithmetic progression, their differences are the same:

(x -7) -(2x +1) = (2x +1) -(x +3)

-x -8 = x -2

-6 = 2x

-3 = x

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The numbers in the sequence are 0, -5, -10.