Sequence given: 2, 5, 8, 11, 14...

Prove that the product of any two consecutive numbers in the sequence can't be in the sequence?

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- Feb 12th 2006, 01:56 PM #1

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- Feb 12th 2006, 04:07 PM #2Originally Posted by
**Natasha**

We want to multiply two consecutive numbers in the series, so use the n and (n+1) terms:

$\displaystyle a_{n+1} * a_n =(3(n+1)+2)(3n+2)=(3n+5)(3n+2)$

$\displaystyle =9n^2+21n+10$

If this is a member of the series, then $\displaystyle (3q+2)=9n^2+21n+10$ for some integer q. Solving for q we obtain:

$\displaystyle q=3n^2+7n+8/3$ which is never an integer for any n.

-Dan

- Feb 13th 2006, 01:51 PM #3

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