WBJEE · Maths · Sequences and Series
Consider the real valued function \(\mathrm{h}:\{0,1,2 \ldots \ldots 100\} \rightarrow \mathrm{R}\) such that \(\mathrm{h}(0)=5, \mathrm{~h}(100)=20\) and satisfying \(h(p)=\frac{1}{2}\{h(p+1)+h(p-1)\}\) for every \(p=1,2 \ldots .99 .\) Then the value of \(h(1)\) is
- A \(5.15\)
- B \(5.5\)
- C 6
- D \(6.15\)
Answer & Solution
Correct Answer
(A) \(5.15\)
Step-by-step Solution
Detailed explanation
\(h(p)=\frac{1}{2}(h(p+1)+h(p-1)) \Rightarrow h(p-1), h(p), h(p+1)\) are in A.P. \(h(100)=h(0)+99 d\) \(\Rightarrow \frac{20-5}{99}=d \Rightarrow d=\frac{15}{99} \Rightarrow h(1)=h(0)+d=5+\frac{15}{99}=5.15\)
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