JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\begin{aligned} S _{ n }( x )=\log _{ a ^{1 / 2}} x +\log _{ a / 3} x +\log _{ a ^{1 / 6}} x \\+\log _{ a ^{1 / 11}} x +\log _{ a ^{1 / 18}} x +\log _{ a ^{1 / 27}} x +\ldots . \end{aligned}\) up to \(n-\)terms, where \(a > 1\). If \(S_{24}(x)=1093\) and \(S _{12}(2 x )=265,\) then value of \(a\) is equal to ..... .
- A \(16\)
- B \(25\)
- C \(9\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
\(S _{ n }( x )=(2+3+6+11+18+27+\ldots \ldots+ n - terms ) \log _{ a } x\) Let \(S _{1}=2+3+6+11+18+27+\ldots .+ T _{ n }\) \(S _{1}=2+3+6+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots+ T _{ n }\) \(T _{ n }=2+1+3+5+\ldots \ldots+ n\) terms…
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