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1959 AMC 12 Question 33

AMC12 · 1959 AMC 12

Question 33

A harmonic progression is a sequence of numbers such that their reciprocals are in arithmetic progression. Let $S_n$ represent the sum of the first $n$ terms of the harmonic progression; for example, $S_3$ represents the sum of the first three terms. If the first three terms of a harmonic progression are $3,$ $4,$ $6,$ then:
  1. $S_4=20$
  2. $S_4=25$
  3. $S_5=49$
  4. $S_6=49$
  5. $S_2=\dfrac12S_4$