Let bi >1 for i = 1, 2, ..., 101. Suppose loge b1, loge b2, , loge b1

1.	Let bi >1 for i = 1, 2, ..., 101. Suppose loge b1, loge b2, , loge b101 are in Arithmetic Progression (A. P.) with the common difference loge 2. Suppose a1, a2, a101 are in A.P. such that a1 b1 and as1 b51. If = t = b1 + b2 +...+ b51 and s = a1 + a2 + ... + a51· then (A) s > t and a101 > b101 (B) s > t and a101 < b101 (C) s < t and a101 > b101 (D) s < t and a101 < b101
Answer» (B) s > t and a₁₀₁ < b₁₀₁ a₂, a₃, ....., a50 are Arithmetic Means and b₂, b₃, ....., b50 are Geometric Means between a₁(= b₁) and a₅₁(= b₅₁) Hence b₂ < a₂, b₃ < a₃ ..... ⇒ t < S Also a₁, a₅₁, a101 is an Arithmetic Progression and b₁, b₅₁, b₁₀₁ is a Geometric Progression Since a₁ = b₁ and a₅₁ = b₅₁ ⇒ b₁₀₁ > a₁₀₁

Let bi >1 for i = 1, 2, ..., 101. Suppose loge b1, loge b2, , loge b101 are in Arithmetic Progression (A. P.) with the common difference loge 2. Suppose a1, a2, a101 are in A.P. such that a1 b1 and as1 b51. If = t = b1 + b2 +...+ b51 and s = a1 + a2 + ... + a51· then (A) s > t and a101 > b101 (B) s > t and a101 < b101 (C) s < t and a101 > b101 (D) s < t and a101 < b101

Answer»

(B) s > t and a₁₀₁ < b₁₀₁

a₂, a₃, ....., a50 are Arithmetic Means and b₂, b₃, ....., b50 are Geometric Means between a₁(= b₁) and a₅₁(= b₅₁)

Hence b₂ < a₂, b₃ < a₃ .....

⇒ t < S

Also a₁, a₅₁, a101 is an Arithmetic Progression and b₁, b₅₁, b₁₀₁ is a Geometric Progression

Since a₁ = b₁ and a₅₁ = b₅₁

⇒ b₁₀₁ > a₁₀₁

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