Which cube members are not in the sequence and prove it? 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?