Pascals Triangle, arithmetic sequence.

[sg001]

Homework Statement

Write down the condition for the numbers p, q, r to form an arithmetic sequence.

Homework Equations

The Attempt at a Solution

Have no idea, but I looked at the answer and they have assigned each letter with a given value (number). How is this possible?

 

[sg001]

sorry the answer is q = 1/2 (p + r)

then they ask for it in a geometric sequence, and the answer to this q^2 = pr

any help would be appreciated... I tried searching the net but they only had examples with numbers containing a certain distance between each other. ie 5,7,9,11...

 

[oli4]

Hi sg001
An arithmetic sequence means for p, q, r that to get q from p, you add a constant.
and to get r from q, you add the same constant.
If you look at p, q, r, (say, put them on a ruler for instance) you will see that q is necessarily in the middle of p and r (since they are separated appart by the same constant).
This is what this answer says.
For a geometric sequence, the same observation holds, except on a logarithmic scale, if you look at the answer and take the logarithm, you will see this is exactly the same formula.

Cheers...

 

[sg001]

Thanks for the help I think I get it now!