question_answer

Let \[{{b}_{i}}>1\] for i =1, 2 ... 101. Suppose\[\log {}_{e}{{b}_{1}}\], \[\log {}_{e}{{b}_{2}},.....,\,\,log{}_{e}{{b}_{101}}\]are in Arithmetic progression (A.P) with the common difference \[\log {}_{e}\] 2. Suppose \[{{a}_{1}},\,{{a}_{2}},\,.....,\,{{a}_{101}}\] are in A.P. such that \[{{a}_{1}}={{b}_{1}}\]and\[{{a}_{51}}={{b}_{51}}\]. If \[t={{b}_{1}}+{{b}_{2}}+.......+{{b}_{51}}\] and \[s={{a}_{1}}+{{a}_{2}}+.....+{{a}_{51}}\] then

A)  \[s>t\,and\,{{a}_{101}}>{{b}_{101}}\]           

B)  \[s>t\,and\,{{a}_{101}}<{{b}_{101}}\]

C)  \[s<t\,and\,{{a}_{101}}>{{b}_{101}}\]           

D)  \[s<t\,and\,{{a}_{101}}<{{b}_{101}}\]

E)  None of these