The three quantities $a, b, c$ are said to be in continued proportion if

b^{2} = a c

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a b = c

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a + b = c

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b^{2} = a + c

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Solution

The correct option is D $b^{2} = a c$
The three quantities $a, b, c$ are said to be in continued proportion if $a : b :: b : c$
$⟹ \frac{a}{b} = \frac{b}{c}$
$⟹ a \times c = b^{2}$
$⟹ b^{2} = a c$

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Similar questions

If three homogeneous quantities a,b and c are in continued proportion, such that $\frac{a}{b} = \frac{b}{c} o r b^{2} = a c o r b = \pm \sqrt{a c}$ , then b is said to be the mean proportional of a and c

If three homogenous quantities a, b, c are in continued proportion such that $\frac{a}{b} = \frac{b}{c}$ , then which of the following is true?

Q. If

a, b, c

are in continued proportion prove that:
(i)

\frac{a^{2} + a b + b^{2}}{b^{2} + b c + c^{2}} = \frac{a}{c}

(ii)

\frac{a^{2} + b^{2} + c^{2}}{{(a + b + c)}^{2}} = \frac{a - b + c}{a + b + c}

Q. If a, b, c are in continued proportion the expression

\frac{a^{2} + a b + b^{2}}{b^{2} + b c + c^{2}}

can be simplified to

Q. If a, b, c are in continued proportion, the expression

\frac{a^{2} + a b + b^{2}}{b^{2} + b c + c^{2}}

can be simplified to

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The three quantities a,b,c are said to be in continued proportion if

The correct option is D b2=acThe three quantities a,b,c are said to be in continued proportion if a:b::b:c⟹ab=bc⟹a×c=b2⟹b2=ac

The three quantities $a, b, c$ are said to be in continued proportion if

The correct option is D $b^{2} = a c$
The three quantities $a, b, c$ are said to be in continued proportion if $a : b :: b : c$
$⟹ \frac{a}{b} = \frac{b}{c}$
$⟹ a \times c = b^{2}$
$⟹ b^{2} = a c$