Divide 36 in six parts which are in arithmetic progression such that the product of the extremes to the product of the means is 1 : 2. Find the numbers.
1
\(\frac{{12}}{7},\;\frac{{24}}{7},\;\frac{{36}}{7},\;\frac{{48}}{7},\frac{{60}}{7},\;\frac{{72}}{7}\)
2
\(\frac{7}{7},\;\frac{{14}}{7},\;\frac{{21}}{7},\;\frac{{28}}{7},\frac{{35}}{7},\;\frac{{42}}{7}\)
3
\(\frac{{10}}{7},\;\frac{{20}}{7},\;\frac{{30}}{7},\;\frac{{40}}{7},\frac{{50}}{7},\;\frac{{60}}{7}\)
4
\(\frac{6}{7},\;\frac{{12}}{7},\;\frac{{18}}{7},\;\frac{{24}}{7},\frac{{30}}{7},\;\frac{{36}}{7}\)