Suppose four distinct positive numbers a 1 , a 2 , a 3 and a 4 are in GP. Let b 1 = a 1 , b 2 = b 1 + a 2 , b 3 = b 2 + a 3 and b 4 = b 3 + a 4 . Statement 1 The numbers

Question

Suppose four distinct positive numbers a 1 ​ , a 2 ​ , a 3 ​ and a 4 ​ are in GP. Let b 1 ​ = a 1 ​ , b 2 ​ = b 1 ​ + a 2 ​ , b 3 ​ = b 2 ​ + a 3 ​ and b 4 ​ = b 3 ​ + a 4 ​ . Statement 1 The numbers b 1 ​ , b 2 ​ , b 3 ​ and b 4 ​ are neither in AP nor in GP. Statement 2 The numbers b 1 ​ , b 2 ​ , b 3 ​ and b 4 ​ are in HP.

TestHub · Accepted Answer

Let a 1 ​ = 1 , a 2 ​ = 2 , a 3 ​ = 4 , a 4 ​ = 8 ∴ b 1 ​ = 1 , b 2 ​ = 3 , b 3 ​ = 7 , b 4 ​ = 15 Clearly, b 1 ​ , b 2 ​ , b 3 ​ and b 4 ​ are not in HP. Statement 2 is false.

Mathematics - Sequence & Series Question with Solution | TestHub

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JEE Main (2026)