JEE Mains · Maths · STD 11 - 8. sequence and series
If \(n\) arithmetic means are inserted between a and \(100\) such that the ratio of the first mean to the last mean is \(1: 7\) and \(a+n=33\), then the value of \(n\) is
- A \(21\)
- B \(22\)
- C \(23\)
- D \(24\)
Answer & Solution
Correct Answer
(C) \(23\)
Step-by-step Solution
Detailed explanation
\(d =\frac{100- a }{ n +1}\) \(A _{1}= a + d\) \(A _{ n }=100- d\) \(\Rightarrow \frac{ A _{1}}{ A _{ n }}=\frac{1}{7} \Rightarrow \frac{ a + d }{100- d }=\frac{1}{7}\) \(\Rightarrow 7 a+8 d=100\) \(\Rightarrow 7\, a +8\left(\frac{100- a }{ n +1}\right)=100\)........\((1)\)…
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