SOLUTION: Given the sequence:2;5;8;.... 1. If the pattern continues ,then write down the next two terms. 2. Prove that none of the terms of this sequence are perfect squares.

Question 1134805: Given the sequence:2;5;8;....
1. If the pattern continues ,then write down the next two terms.
2. Prove that none of the terms of this sequence are perfect squares.
Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.

Arithmetic sequence with the first term 2 and the common difference 3.


 = 2 + 3*(n-1).


The next two terms are  11  and  14.



When divided by 3, every term gives the remainder of 2.

Therefore, neither term of this sequence is a square, because a square of an integer number NEVER gives remainder 2 when divided by 3.


It gives the remainders 0 or 1, but never gives the remainder 2.

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