Prove that , and can't be terms in the same

- arithmetic
- geometric

progression.

- Jan 5th 2008, 11:30 AMjames_bondsqrt 2, sqrt 3, sqrt 5 can't be in the same arithmetic/geometric progression
Prove that , and can't be terms in the same

- arithmetic
- geometric

progression. - Jan 5th 2008, 11:55 AMjanvdl
- Jan 5th 2008, 01:33 PMmr fantastic
- Jan 5th 2008, 08:11 PMThePerfectHacker
- Jan 5th 2008, 11:30 PMjames_bond
But they don't have to be neighbors!

- Jan 5th 2008, 11:37 PMmr fantastic
- Jan 6th 2008, 01:49 AMjanvdl
- Jan 6th 2008, 01:50 AMred_dog
Suppose are not consecutive terms of an arithmetic or geometric progression.

For the arithmetic progression:

Let (1)

(2)

(3)

Substracting (2) from (1) and (3) from (2) we get

Then

But, the left side member is irational and the right side member is rational.

For the geometric progression:

Let (1)

(2)

(3)

Then

The last equality is not true. - Jan 6th 2008, 02:04 AMjanvdl
- Jan 6th 2008, 03:06 AMIsomorphism
- Jan 6th 2008, 07:33 AMjanvdl
- Jan 6th 2008, 10:33 AMThePerfectHacker
It is just that you were doing a different problem than Red_dog. You were saying that sqrt(2),sqrt(3),sqrt(5) cannot be right next to each other, and what you did is correct. But Red_dog did a stronger problem he showed that you cannot have these three numbers in any arithmetic progession. Meaning you cannot have sqrt(2) as a 3rd term, sqrt(3) as a 10th term, and sqrt(5) as a 29th term.