Question
Show that the following numbers are in continued proportion: $16, 84, 441$
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Answer
$16, 84, 441$
$\Rightarrow\frac{16}{84}=\frac{84}{441}$
$\Rightarrow\frac{16\div4}{84\div4}=\frac{84\div21}{441\div21}$
$\Rightarrow\frac{4}{21}=\frac{4}{21}$
$\therefore 16, 84, 441$ are in continued proportion.
$\Rightarrow\frac{16}{84}=\frac{84}{441}$
$\Rightarrow\frac{16\div4}{84\div4}=\frac{84\div21}{441\div21}$
$\Rightarrow\frac{4}{21}=\frac{4}{21}$
$\therefore 16, 84, 441$ are in continued proportion.
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