Which cube members are not in the sequence and prove it?(adsbygoogle = window.adsbygoogle || []).push({});

2, 5, 8, 11, 14, ...

How can this be proved

My answer:

an = 3n + 2

Any natural number may be written as N= 3k+p for some natural number K and p=0,1 or 2.

So

N^3=(3k+p)3

N^3=3(9k+k^2p+kp^2)+p^3

N^3=3k+p^3

Therefore N^3 (mod 3)

So as an is congruent to 2(mod 3), N^3 lies in the sequence. In other words, the cude of any number in the sequence is in the sequence.But how do I go and show which cube members are not in the sequence and moreover how do I prove it?

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# Homework Help: Which cube members are not in the sequence and prove it?

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