Let bi>1 for i=1,2,...,101. Suppose logeb1,logeb2,...,logeb101 are in Arithmetic Progression (A.P.) with the common difference loge2. Suppose a1,a2,...,a101 are in A.P. such that a1=b1 and a51=b51. If t=b1+b2+⋯+b51 and s=a1+a2+⋯+a51, then

Let bi>1 for i=1,2,...,101. Suppose logeb1,logeb2,...,logeb101 are in

1.	Let bi>1 for i=1,2,...,101. Suppose logeb1,logeb2,...,logeb101 are in Arithmetic Progression (A.P.) with the common difference loge2. Suppose a1,a2,...,a101 are in A.P. such that a1=b1 and a51=b51. If t=b1+b2+⋯+b51 and s=a1+a2+⋯+a51, then
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 $t = b_{1} + b_{2} + \dots + b_{51} and s = a_{1} + a_{2} + \dots + a_{51},$ then