如果数列{an}满足a1,a2/a1,a3/a2,...an/an-1,...是首项为1,公比为2的等比数列,则a101等于（）

题目

如果数列{an}满足a1,a2/a1,a3/a2,...an/an-1,...是首项为1,公比为2的等比数列,则a101等于（）

答案

a1 = 1; a2/a1 = 2; => a2 = a1*2; => a2 = 2;a3/a2 = 4; => a3 = a2*4; => a3 = 8;.证明：因为 ai/a(i-1) = 2^(i-1); (i>=2)=> ai = 2^(i-1)* a(i-1)=> ai = 2^(i-1)*2^(i-2)*a(i-2);.这里可以顺次展开,一直展开到2...