Question 922288
I understand the first term to be the positive number {{{1/2}}} .
We need an arithmetic progression, where each term differs from the one before by a common difference {{{d}}} .
The first term is {{{2}}} , which is followed by 3 more terms, and then by {{{14}}} .
The terms are {{{2}}} , {{{2+d}}} , {{{2+2d}}} , {{{2+3d}}} , {{{14}}}
The fifth term is {{{2+(5-1)d=2+4d=14}}} .
{{{2+4d=14}}}--->{{{4d=14-2}}}--->{{{4d=12}}}--->{{{d=12/4}}}--->{{{d=3}}} .
So the terms of the arithmetic progression are
{{{2}}} , {{{2+3=5}}} , {{{5+3=8}}} , {{{8+3=11}}} , {{{11+3=14}}} ,
and the terms of the harmonic progression are
{{{1/2}}} , {{{1/5}}} , {{{1/8}}} , {{{1/11}}} , and {{{1/14}}} .
 
NOTE: If the first term was {{{-1/2}}} ,
then the arithmetic progression would be
{{{-2}}} , {{{2}}} , {{{6}}} , {{{10}}} , {{{14}}} ,
and the harmonic progression would be
{{{-1/2}}} , {{{1/2}}} , {{{1/6}}} , {{{1/10}}} , {{{1/14}}} .