Consider
![\[a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a3ab43dca3872e69a0c1be257c1ecec8_l3.png "Rendered by QuickLaTeX.com")
to be the initial term and r to be the normal proportion of the G.P.
Given,
![\[{{S}_{2}}~=\text{ }-4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4cf39d1c5619f0cffddcf6b8ae06ece5_l3.png "Rendered by QuickLaTeX.com")
Then, at that point, from the inquiry we have
Also,
![\[\begin{array}{*{35}{l}} {{a}_{5}}~=\text{ }4\text{ }x\text{ }{{a}_{3}} \\ a{{r}^{4}}~=\text{ }4a{{r}^{2}} \\ {{r}^{2}}~=\text{ }4 \\ r\text{ }=\text{ }\pm \text{ }2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b27faa4c2cdf1fb69554cda04c97b741_l3.png "Rendered by QuickLaTeX.com")
Utilizing the worth of r in (1), we have
In this way, the necessary G.P is
![\[-4/3,\text{ }-8/3,\text{ }-16/3,\text{ }\ldots .\text{ }Or\text{ }4,\text{ }-8,\text{ }16,\text{ }-32,\text{ }\ldots \ldots \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f6e116c115f953ddd058d53ef1707779_l3.png "Rendered by QuickLaTeX.com")
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.