JEE Mains · Maths · STD 11 - 8. sequence and series
For a natural number \(n\), let \(a _{ n }=19^{ n }-12^{ n }\). Then, the value of \(\frac{31 \alpha_{9}-\alpha_{10}}{57 \alpha_{8}}\) is
- A \(2\)
- B \(3\)
- C \(5\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(a _{ n }=19^{ n }-12^{ n }\) \(\frac{31 \alpha_{9}-\alpha_{10}}{57 \alpha_{8}}=\frac{31\left(19^{9}-12^{9}\right)-\left(19^{10}-12^{10}\right)}{57 \alpha_{8}}\) \(=\frac{19^{9}(31-19)-12^{9}(31-12)}{57 \alpha_{8}}\) \(=\frac{19^{9} \cdot 12-12^{19} \cdot 19}{57 \alpha_{8}}\)…
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