Question

5. Find the common ratio of GP root 2,root8,root32, .....
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Answer 1

$\textbf{Given:}$

$\textsf{G.P is}$

$\mathsf{\sqrt{2},\;\sqrt{8},\;\sqrt{32}\;.\;.\;.\;.\;.}$

$\textbf{To find:}$

$\textsf{Common ratio of the G.P}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\sqrt{2},\;\sqrt{8},\;\sqrt{32}\;.\;.\;.\;.\;.}$

$\underline{\mathsf{Common\;ratio:}}$

$\mathsf{r=\dfrac{\sqrt{8}}{\sqrt{2}}}$

$\mathsf{r=\dfrac{\sqrt{4{\times}2}}{\sqrt{2}}}$

$\mathsf{r=\dfrac{\sqrt{4}\sqrt{2}}{\sqrt{2}}}$

$\mathsf{r=\dfrac{2\sqrt{2}}{\sqrt{2}}}$

$\implies\boxed{\mathsf{r=2}}$

$\therefore\textsf{The common rtaio is 2}$

$\textbf{Find more:}$

Find the common ratio of GP 2 2 root 2 4 . . .

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What is the common ratio for the geometric sequence below, written as a fraction?

768, 480, 300, 187.5, . . .

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