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Ratio of Sums of an Arithmetic Sequence

Source: 2022 AMC 10B #15

November 17, 2022
ratioarithmetic sequence

Problem Statement

Let SnS_n be the sum of the first nn term of an arithmetic sequence that has a common difference of 22. The quotient S3nSn\frac{S_{3n}}{S_n} does not depend on nn. What is S20S_{20}?
<spanclass=′latex−bold′>(A)</span>340<spanclass=′latex−bold′>(B)</span>360<spanclass=′latex−bold′>(C)</span>380<spanclass=′latex−bold′>(D)</span>400<spanclass=′latex−bold′>(E)</span>420<span class='latex-bold'>(A) </span> 340 \qquad <span class='latex-bold'>(B) </span> 360 \qquad <span class='latex-bold'>(C) </span> 380 \qquad <span class='latex-bold'>(D) </span> 400 \qquad <span class='latex-bold'>(E) </span> 420
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