Number Systems -Sequence and Series

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sukhman: Master | Next Rank: 500 Posts; Posts: 202; Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members; Thanked: 3 times

by sukhman » Thu Oct 17, 2013 8:21 am

The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1240. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A) 2480 (B) 3490 (C) 6785 (D) 8215 (E) 9255

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Source: Beat The GMAT — Problem Solving | Thu Oct 17, 2013 8:21 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Thu Oct 17, 2013 8:51 am

Sum of next 15 terms = sum of 30 terms - sum of 15 terms

Using formula: (n)(n+1)(2n+1)/6

= (30)(31)(61)/6 - 1240
= 8215

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