Problem: A harmonic progression is a sequence of numbers such that their reciprocals are in arithmetic progression. Let Sn represent the sum of the first n terms of the harmonic progression; for example, S3 represents the sum of the first three terms. If the first three terms of a harmonic progression are 3,4,6, then:
Answer Choices:
A. S4=20
B. S4=25
C. S5=49
D. S6=49
E. S2=1/2S4
Solution:
31,41,161,121,0 with d=−121
therefore the terms of the H.P. are 3,4,6,12 only ∴S4=25