Find the sum of first 25 terms of the sequence 16,24,32
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a = 16
d = 24-16 = 8
Let number of terms = n
Sn =n{2xa+n-2xd } /2
=n{2x16+(n-1)x8}
= 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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