If the ratio of the sum of first $n$ terms of two APs is $(7 n + 1) : (4 n + 27)$ , find the ratio of their 9th terms.

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If two positive integers $a$ and $b$ are written as $a = x^{3} y^{2}$ and $b = x y^{3}$ , where $x$ and $y$ are prime numbers, what is the…
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