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1967 AMC 12 Question 39

AMC12 · 1967 AMC 12

Question 39

Given the sets of consecutive integers $\{1\},$ $\{2,3\},$ $\{4,5,6\},$ $\{7,8,9,10\},$ $\ldots,$ where each set contains one more element than the preceding one, and where the first element of each succeeding set is one more than the last element of the preceding set. Let $S_n$ be the sum of the elements in the $n$th set. Then $S_{21}$ equals:
  1. $1113$
  2. $4641$
  3. $5082$
  4. $53361$
  5. none of these