If a_ 1 , a_ 2 , a_ 3 , .........., a_ n are in H.P. then a_ 1 a_ 2 +a_ 3 + +a_ n , a_ 2…
Mathematics · JEE Main · NTA Exams — Progression and Series
If \(a_{1}, a_{2}, a_{3},\).........., \(a_{n}\) are in H.P. then
\(\frac{a_{1}}{a_{2}+a_{3}+\ldots+a_{n}}, \frac{a_{2}}{a_{1}+a_{3}+\ldots+a_{n}}, \frac{a_{3}}{a_{1}+a_{2}+a_{4}+\ldots+a_{n}},\)
\(\ldots ., \frac{a_{n}}{a_{1}+a_{2}+\ldots .+a_{n-1}}\) are in
\(\frac{a_{1}}{a_{2}+a_{3}+\ldots+a_{n}}, \frac{a_{2}}{a_{1}+a_{3}+\ldots+a_{n}}, \frac{a_{3}}{a_{1}+a_{2}+a_{4}+\ldots+a_{n}},\)
\(\ldots ., \frac{a_{n}}{a_{1}+a_{2}+\ldots .+a_{n-1}}\) are in
- A.P.
- G.P.
- H.P.
- A.G.P.
Answer
(C) H.P.
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