Series Question (1 Viewer)

[DJel]

Hi,

the question is;

Three consecutive terms in an arithmetic series are x, x², and 5x.

(i) Show that; 2x² - 6x = 0
(ii) Find the common difference.
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Thanks,

DJel.

 

[minijumbuk]

i) Since it is an AP, then:
5x-x² = x² = x
Collect like terms, and bring everything to one side, you get 2x² - 6x = 0

ii) Solve for x: 2x(x-3) = 0
That means x = 0, or x=3
But if x=o, then it's not a series, so x must be =3
Now, substituting x=3 into x, x², 5x, you get these values:
3, 9, 15
And therefore the common difference is 6.

 

[DJel]

Awesome, thanks for the solution.