## 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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