- #1
Natasha1
- 493
- 9
Right here is my sequence 2, 5, 8, 11, 14, ...
I have been asked to prove that the cube of any number in the sequence is 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 show which cube numbers (therefore not in the sequence, I think ) are not in the sequence and to prove it?
A little confused how to do this one could anyone help please :-)
I have been asked to prove that the cube of any number in the sequence is 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 show which cube numbers (therefore not in the sequence, I think ) are not in the sequence and to prove it?
A little confused how to do this one could anyone help please :-)
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