The necessary aggregate
![\[=~2\text{ }x\text{ }128\text{ }+\text{ }4\text{ }x\text{ }32\text{ }+\text{ }8\text{ }x\text{ }8\text{ }+\text{ }16\text{ }x\text{ }2\text{ }+\text{ }32\text{ }x\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e055a129317660fbf93c8a9db447b41_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }64[4\text{ }+\text{ }2\text{ }+\text{ }1\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }+\text{ }1/{{2}^{2}}]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0fc2e911208e1c38a8500918f39f8b13_l3.png "Rendered by QuickLaTeX.com")
Presently, it’s seen that
![\[4,\text{ }2,\text{ }1,~{\scriptscriptstyle 1\!/\!{ }_2},\text{ }1/{{2}^{2}}~is\text{ }a\text{ }G.P.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f6c7fb99d0b696c32d58eb8e8344efc_l3.png "Rendered by QuickLaTeX.com")
With initial term,
![\[a\text{ }=\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ac1222b81394580973acc531cc4c93c9_l3.png "Rendered by QuickLaTeX.com")
Normal proportion,
![\[r\text{ }=1/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-65491d8cc85b27583062be5e317a0f48_l3.png "Rendered by QuickLaTeX.com")
We know,
Accordingly, the necessary aggregate
![\[=~64\left( 31/4 \right)\text{ }=\text{ }\left( 16 \right)\left( 31 \right)\text{ }=\text{ }496\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-82e6894c81184727e08309e24ebf7a8a_l3.png "Rendered by QuickLaTeX.com")
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2.
Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2.