Q79 / 180 · KCET 2009 · Mathematics

$\lim _{n \rightarrow \infty} \frac{3 \cdot 2^{n+1}-4 \cdot 5^{n+1}}{5 \cdot 2^{n}+7 \cdot 5^{n}}$ is equal to

  • A
    $\frac{3}{5}$
  • B
    $-\frac{4}{7}$
  • Correct answer
    C
    $-\frac{20}{7}$
  • D
    0

Solution

$\begin{aligned} \lim _{n \rightarrow \infty} \frac{3 \cdot 2^{n+1}-4 \cdot 5^{n+1}}{5 \cdot 2^{n}+7 \cdot 5^{n}} \\ &=\lim _{n \rightarrow \infty} \frac{5^{n}\left(6 \cdot\left(\frac{2}{5}\right)^{n}-20\right)}{5^{n}\left(5 \cdot\left(\frac{2}{5}\right)^{n}+7\right)} \\ &=-\frac{20}{7} \end{aligned}$

Hence, the correct answer is option: 'C'.

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