例1设S_n是等比数列{a_n}的前n项和,a_n>0,若S_6-2S_3=5,则S9-S6的最小值为____.分析本题的常规解法是基本量法,即先由已知条件得到首项a_1与公比q的关系,再用a_1或q表示S_9-S_6,从而求出S_9-S_6的最小值.如果将S_3看成一个整体,设S_3=m,将S_9-S_6表示成m的函数,解题过程就更加简捷.这 Example 1 Let S_n be the first n terms of the geometric series {a_n} and, a_n> 0, if S_6-2S_3 = 5, then the minimum value of S9-S6 is ____. Analysis The general solution to this question is the basic method, Firstly, we get the relationship between the first a_1 and the public ratio q by the known conditions, and then use S_1 or q to represent S_9-S_6 to find the minimum value of S_9-S_6. If S_3 is regarded as a whole, let S_3 = m, S_9-S_6 expressed as a function of m, the problem-solving process is more simple