Q9 of 50 Page 32

Prove that the sum of any number of terms of the arithmetic sequence 16, 24, 32, … starting from the first, added to 9 gives a perfect square.

a = 16


d = 24-16 = 8


Let number of terms = n


Sn =


=


= n(12 + 4n)


Sn + 9 = 4n2 + 12n + 9 = (2n + 3)2


Hence, the sum of any number of terms of the arithmetic sequence 16, 24, 32, …. starting from the first, added to 9 gives a perfect square.


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