Please solve this question as attached in the image. I am not getting the proper solution

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Aditya Gupta · Answer

so we can write f k = S n – na k or f k /a k =S n /a k – n, where Sn = sum of a1, a2, …., an or 1/ α k = S n /a k – n now, 1/ α k – 1/ α k-1 = S n *(1/ a k – 1/a k-1 ) but 1/ a k – 1/a k-1 = d (a constant coz a1, a2, …., an are in HP) So, 1/ α k – 1/ α k-1 = S n *d = constant so α 1, α 2, α 3, …. are in HP too So, obviously 2^ α 1, 2^ α 2, 2^ α 3,.... , 2^ α n are neither in GP (coz 2^ α k /2^ α k-1 is not a constant), nor in AP, and also not in HP so correct option is none of these.

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Please solve this question as attached in the image. I am not getting the proper solution

Please solve this question as attached in the image. I am not getting the proper solution

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Please solve this question as attached in the image. I am not getting the proper solution

Please solve this question as attached in the image. I am not getting the proper solution

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