Q10 of 50 Page 26

Prove that the arithmetic sequence 5, 8, 11, … contains no perfect squares.

a = 5


d = 8-5 = 3


an = a + (n-1) × d


an = 5 + (n-1) × 3


∴ an = 3n + 2


Let p be a natural number


p2 = 3n + 2


n =


Now, for all integers from 0 to 9(i.e. p from 0 to 9), n does not come out to be an integer.


Hence, the arithmetic sequence 5, 8, 11, … contains no perfect squares.


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