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JEE Advanced 2016 Paper 2 Mathematics Question 38

Let \(b_i > 1\) for \(i = 1, 2, \dots, 101\). Suppose \(\text{log}_e{b_1}, \text{log}_e{b_2}, \dots, \text{log}_e{b_{101}}\) are in Arithmetic Progression (A.P.) with the common difference \(\text{log}_e{2}\). Suppose \(a_1, a_2, \dots, a_{101}\) are in A.P. such that \(a_1 = b_1\) and \(a_{51} = b_{51}\). If \(t = b_1 + b_2 + \dots + b_{51}\) and \(s = a_1 + a_2 + \dots + a_{51}\), then

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