已知有一列数x1,x2,x3,...,x7,且x1=8,x7=5832,x1/x2=x2/x3=x3/x4=x4/x5=x5/x6=x6/x7=x7/x8,求x5的值,

问题描述:

已知有一列数x1,x2,x3,...,x7,且x1=8,x7=5832,x1/x2=x2/x3=x3/x4=x4/x5=x5/x6=x6/x7=x7/x8,求x5的值,

x5=648

x1=8;x2=24;x3=72;x4=216;x5=648;x6=1944;x7=5832;x8=17496

由条件可知,该数列为等比数列
X7=X1*q^6=8*q^7=5832
得q=3
X5=X1*q^4=8*3^4=8*81=648