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  4. The sum of 152+162+172+.....+302 is equal to:

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Q. The sum of $ {{15}^{2}}+{{16}^{2}}+{{17}^{2}}+.....+{{30}^{2}} $ is equal to:

KEAMKEAM 2004

Solution:

$ {{15}^{2}}+{{16}^{2}}+{{17}^{2}}......+{{30}^{2}} $ $ ={{1}^{2}}+{{2}^{2}}+...+{{30}^{2}}-({{1}^{2}}+{{2}^{2}}+....+{{14}^{2}}) $
$ =\frac{30(31)(61)}{6}-\frac{14(15)(29)}{6} $
$ =\frac{56730-6090}{6}=8440 $