Homework Help: Arithmetic sequences

1. Nov 29, 2009

Faiien

1. The problem statement, all variables and given/known data

Find x so that x+5, 3x+1, and 4x+1 are consecutive terms of an arithmetic sequence.

Not really sure how to do the problem at all. Some assistance would be much appreciated.

2. Nov 29, 2009

Hurkyl

Staff Emeritus
Re: Sequences

What do you know about "three consecutive terms in an arithmetic sequence"?

3. Nov 29, 2009

Faiien

Re: Sequences

Because it's an arithmetic sequence, if you add a constant to one solution you can get the next solution.

4. Nov 29, 2009

Hurkyl

Staff Emeritus
Re: Sequences

"solution"? Did you mean "term"?

What do you know about three consecutive terms in a sequence?

P.S. this is algebra. Name things with variables. Express facts as equations.

5. Nov 29, 2009

Faiien

Re: Sequences

Yes, I apologize, I did mean terms.
Because the terms of an arithmetic sequence always vary by a constant
x+a, x+2a. x+3a
you can attain a, the constant, by subtracting two consecutive terms.
(x+2a)-(x+a)=a or (x+3a)-(x+2a)=a

6. Nov 29, 2009

Hurkyl

Staff Emeritus
Re: Sequences

Let's not use 'x' here! We're already using 'x' for something else!

So we know "three consecutive terms of an arithmetic sequence" can be written as
r+a, r+2a, r+3a​
for an appropriate choice of r and a.

So now, how do you express the fact that
x+5, 3x+1, and 4x+1 are "three consecutive terms of an arithmetic sequence"​
?