Interesting problem involving arithmetic progression

Bipolarity

I just came up with a problem I hope you will find interesting, but I can't seem it solve it myself. I thought of induction as some guide, but am not sure how to proceed.

There are N terms in some finite arithmetic progression. Two of those terms are equal to 3. Prove that all terms in this progression also equal 3.

BiP

Simon Bridge

You are making life too hard for yourself :)

An arithmetic progression is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

If term x_i=a and x_i+n=b then the difference between successive terms Δx must be Δx=(b-a)/n.

If a=b then Δx must be ...

Bipolarity

Thanks!

So 2=2+n*d
0 = n*d
d = 0, since n is not 0.

Since d=0, every term must equal the ith term, which happens to be 2!

Genius!

BiP

Mark44

I'm assuming that the work above is related to the problem in the original post. The i-th term can't be 2 if you're proving that all the terms in the progression are 3.

Bipolarity

Sorry my mistake, I meant to write 3.

BiP