in a certain geometric sequence the first term exceeds the second term by 32 and the sum of the seco

题目

in a certain geometric sequence the first term exceeds the second term by 32 and the sum of the second and third is 48,find the infinite sum of rhe sequence

答案

一个几何级数中,第一项比第二项大32,第二项与第三项的和是48,求这个级数的无穷和.
设几何级数的前三项是a,aq,aq^2,则
a-aq=32,aq+aq^2=48,解得
a=8,q=-3,这时无穷和发散,
a=64,q=1/2,这时a+aq+aq^2+...=64/(1-1/2)=128.