The necessary aggregate \[=~2\text{ }x\text{ }128\text{ }+\text{ }4\text{ }x\text{ }32\text{ }+\text{ }8\text{ }x\text{ }8\text{ }+\text{ }16\text{ }x\text{ }2\text{ }+\text{ }32\text{ }x\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]
\[=\text{ }64[4\text{ }+\text{ }2\text{ }+\text{ }1\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }+\text{ }1/{{2}^{2}}]\]
Presently, it’s seen that
\[4,\text{ }2,\text{ }1,~{\scriptscriptstyle 1\!/\!{ }_2},\text{ }1/{{2}^{2}}~is\text{ }a\text{ }G.P.\]
With initial term, \[a\text{ }=\text{ }4\]
Normal proportion, \[r\text{ }=1/2\]
We know,
Accordingly, the necessary aggregate\[=~64\left( 31/4 \right)\text{ }=\text{ }\left( 16 \right)\left( 31 \right)\text{ }=\text{ }496\]