Prove an arithmetic

[mattgad]

The first three terms of an arithmetic series are p, 5p - 8, and 3p + 8. Show that p = 4.

I'm not sure how to tackle this one. Can anyone start me off on what I need to do to prove it?

I had a reply about this in another thread, (5p−8)−(p)=(3p+8)−(5p−8), but I do not understand why I would do this.

Thanks.

 

[Unco]

An arithmetic series increases by the same amount each term

e.g 1, 3, 5, 7, 9....
See how it has increased by 2 each term?

So the difference of your first terms (5p - 8) - p

And this must equal the difference between the second and third terms:
(3p + 8) - (5p - 8)

That is where your equation comes from to solve for p.

P.S: Please reply to replies in the same thread.

 

[mattgad]

I see what you mean.

It's:
2nd term - 1st term = 3rd term - 2nd,

Thanks for clearing that up.

 

[Denis]

The first three terms of an arithmetic series are p, 5p - 8, and 3p + 8. Show that p = 4.
I'm not sure how to tackle this one. Can anyone start me off on what I need to do to prove it?
I had a reply about this in another thread, (5p−8)−(p)=(3p+8)−(5p−8), but I do not understand why I would do this. Thanks.

Well, 1st and 3rd terms must equal twice the 2nd, so:
p + 3p+8 = 2(5p - 8)
4p + 8 = 10p - 16
6p = 24
p = 4