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?
The sequence is arithmatic, with a separation of 3 and initial value of 2. So we may model the series as .Originally Posted by Natasha
We want to multiply two consecutive numbers in the series, so use the n and (n+1) terms:
If this is a member of the series, then for some integer q. Solving for q we obtain:
which is never an integer for any n.