Right here is my sequence 2, 5, 8, 11, 14, ....(adsbygoogle = window.adsbygoogle || []).push({});

I have been asked to prove thatthe cube of any number in the sequenceis in the sequence.

my answer:

General term: a_n=3n+2

We need to cube a_n and see if it matches a number in the series i.e. (a_n)^3 = 3q+2 for some integer q.

(a_n)^3

=27n^3 + 54n^2 + 36n + 8

=3(9n^3 + 18n^2 + 12n + 2) +2

=3k+2

If this is a member of the series, then 3q+2 = 3k+2 for some integer q.

Solving for q:

q = k which is always in the sequence.

So the cube of any number is in this sequence.

But now I'm asked to showwhich cube numbers(therefore not in the sequence, I think )are notin the sequence and to prove it?

A little confused how to do this one could anyone help please :-)

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# Homework Help: Sequence and series

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