Question

URGENT! WILL GIVE MEDAL! PLEASE SHOW STEPS OF WORKING OUT! Find x if 3-x^2, -2x and 1-x are consecutive terms of an arithmetic sequence.

Answer 1

Use the concept of a generic arithmetic sequence; the difference between two sequential terms must be equal to d

Therefore,

3-x^2+d=-2x and,
-2x +d = 1-x

Solve for d:

3-x^2+d=-2x ---> d=x^2 - 2x-3

-2x +d = 1-x ---> d= 1 +x

Now solve for x:

x^2 - 2x-3= 1 +x ---> x^2-3x-4=0

Factor out:

(x-4)(x+1)

Therefore x= 4, -1

Answer 2

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