If $a,\;b,\;c$ are in $G.P.$, then
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
Similar Questions
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The remainder when the polynomial $1+x^2+x^4+x^6+\ldots+x^{22}$ is divided by $1+x+x^2+x^3+\ldots+x^{11}$ is
- [KVPY 2016]
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If the roots of the cubic equation $a{x^3} + b{x^2} + cx + d = 0$ are in $G.P.$, then
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Find the $20^{\text {th }}$ and $n^{\text {th }}$ terms of the $G.P.$ $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \ldots$
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Let $a_1, a_2, a_3, \ldots .$. be a sequence of positive integers in arithmetic progression with common difference $2$. Also, let $b_1, b_2, b_3, \ldots .$. be a sequence of positive integers in geometric progression with common ratio $2$ . If $a_1=b_1=c$, then the number of all possible values of $c$, for which the equality
$2\left(a_1+a_2+\ldots .+a_n\right)=b_1+b_2+\ldots . .+b_n$
holds for some positive integer $n$, is. . . . . . .
Let $a_1, a_2, a_3, \ldots .$. be a sequence of positive integers in arithmetic progression with common difference $2$. Also, let $b_1, b_2, b_3, \ldots .$. be a sequence of positive integers in geometric progression with common ratio $2$ . If $a_1=b_1=c$, then the number of all possible values of $c$, for which the equality
$2\left(a_1+a_2+\ldots .+a_n\right)=b_1+b_2+\ldots . .+b_n$
holds for some positive integer $n$, is. . . . . . .
- [IIT 2020]