Let a 1 , a 2 , a 3 … , a 10 be in G . P . with a i 0 for i = 1 , 2 , … , 10 and S be the set of pairs r , k , r , k ∈ N (the set of natural numbers) for which log e ⁡ a 1 r a 2 k log e ⁡ a 2 r a 3 k log e ⁡ a 3 r a 4 k log e ⁡ a 4 r a 5 k log e ⁡ a 5 r a 6 k log e ⁡ a 6 r a 7 k log e ⁡ a 7 r a 8 k log e ⁡ a 8 r a 9 k log e ⁡ a 9 r a 10 k = 0 Then the number of elements in S , is:

Question

Let a 1 , a 2 , a 3 … , a 10 be in G . P . with a i > 0 for i = 1 , 2 , … , 10 and S be the set of pairs r , k , r , k ∈ N (the set of natural numbers) for which log e ⁡ a 1 r a 2 k log e ⁡ a 2 r a 3 k log e ⁡ a 3 r a 4 k log e ⁡ a 4 r a 5 k log e ⁡ a 5 r a 6 k log e ⁡ a 6 r a 7 k log e ⁡ a 7 r a 8 k log e ⁡ a 8 r a 9 k log e ⁡ a 9 r a 10 k = 0 Then the number of elements in S , is:, Infinitely many, 4, 10, 2

MARKS App · Accepted Answer

C 3 → C 3 - C 2 , C 2 → C 2 - C 1 ( Let α is common ratio of G P ) l o g e a 1 r a 2 k l o g e α r + k l o g e α r + k l o g e a 4 r a 5 k l o g e α r + k log e ⁡ α r + k l o g e a 7 r a 8 k log e ⁡ α r + k log e ⁡ α r + k = 0 which is always true because C 2 & C 3 are identical.

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