If a,b,c are in G.P. , then

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8. Sequences and Series

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If $a,\;b,\;c$ are in $G.P.$, then

A

${a^2},\;{b^2},\;{c^2}$ are in $G.P.$

B

${a^2}(b + c),\;{c^2}(a + b),\;{b^2}(a + c)$ are in $G.P.$

C

$\frac{a}{{b + c}},\;\frac{b}{{c + a}},\;\frac{c}{{a + b}}$ are in $G.P.$

D

None of the above

Solution

(a) $a ,b ,c$ are in $G.P.$

$\therefore \;\frac{b}{a} = \frac{c}{b} = r$

$ \Rightarrow $$\frac{{{b^2}}}{{{a^2}}} = \frac{{{c^2}}}{{{b^2}}} = {r^2}$

$ \Rightarrow $${a^2},\,\;{b^2},\;{c^2}$ are in $G.P.$

Standard 11

Mathematics

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