Three numbers are in an increasing geometric progression with common ratio \(r\). If the middle number is doubled, then the new numbers are in arithmetic progression with common difference \(d\). If the fourth term of GP is \(3r^{2}\) then \(r^{2} - d\) is equal to ?

[JEE Main 2021, 31 Aug (Shift 1)]

Question

Three numbers are in an increasing geometric progression with common ratio \(r\). If the middle number is doubled, then the new numbers are in arithmetic progression with common difference \(d\). If the fourth term of GP is \(3r^{2}\) then \(r^{2} - d\) is equal to ?

[JEE Main 2021, 31 Aug (Shift 1)]

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Three numbers are in an increasing geometric progression with common ratio \(r\). If the middle number is doubled, then …

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