Question

# If n arithmetic means a1,a2,...,an are inserted between 50 and 200 and n harmonic means h1,h2,...,hn are inserted between the same two numbers, then (a2hn−1÷2000) is equal to

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Solution

## 50,a1,a2,...,an,200 are in A.P., ...(1)And50,h1,h2,...,hn,200 are in H.P.,⇒150,1h1,1h2,...,1hn,1200 are in A.P.Reversing it, we get 1200,1hn,1hn−1,...,1h1,150 are in A.P. ...(2)Multiplying (2) by 10000, we get50,10000hn,10000hn−1,...,10000h1,200 are in A.P. ... (3)(1) and (3) are identical, ∴a2=10000hn−1⇒a2hn−1=10000Hence, answer is 10000.So, a2hn−1÷2000=5

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