For a natural number n,let a_{n} = 19^{n} - 1 | vedclass

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(D) Given $a_{n} = 19^{n} - 12^{n}$.We need to evaluate the expression $E = \frac{31 a_{9} - a_{10}}{57 a_{8}}$.Substitute $a_{9} = 19^{9} - 12^{9}$ a

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$4$

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(D) Given $a_{n} = 19^{n} - 12^{n}$.We need to evaluate the expression $E = \frac{31 a_{9} - a_{10}}{57 a_{8}}$.Substitute $a_{9} = 19^{9} - 12^{9}$ and $a_{10} = 19^{10} - 12^{10}$:$E = \frac{31(19^{9} - 12^{9}) - (19^{10} - 12^{10})}{57 a_{8}}$Rearrange the terms:$E = \frac{31 \cdot 19^{9} - 31 \cdot 12^{9} - 19^{10} + 12^{10}}{57 a_{8}}$Group the terms with $19$ and $12$:$E = \frac{19^{9}(31 - 19) - 12^{9}(31 - 12)}{57 a_{8}}$Simplify the coefficients:$E = \frac{19^{9}(12) - 12^{9}(19)}{57 a_{8}}$Factor out $12 \cdot 19$ from the numerator:$E = \frac{12 \cdot 19(19^{8} - 12^{8})}{57 a_{8}}$Since $57 = 3 \cdot 19$,we have $57 a_{8} = 3 \cdot 19(19^{8} - 12^{8})$:$E = \frac{12 \cdot 19(19^{8} - 12^{8})}{3 \cdot 19(19^{8} - 12^{8})}$$E = \frac{12}{3} = 4$.

For a natural number $n$,let $a_{n} = 19^{n} - 12^{n}$. Then,the value of $\frac{31 a_{9} - a_{10}}{57 a_{8}}$ is

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