s10=10,s30=70.s40=?等比数列

题目

s10=10,s30=70.s40=?等比数列

答案

S10=a1(1-q^10)/(1-q)=10
S30=a1(1-q^30)/(1-q)=70
两式相除
(1-q^30)/(1-q^10)=7
1+q^10+q^20=7
(q^10+3)(q^10-2)=0
q^10>0
所以q^10=2
S40=a1(1-q^40)/(1-q)
=a1(1-q^20)(1+q^20)/(1-q)
=a1(1-q^10)(1+q^10)(1+q^20)/(1-q)
=[a1(1-q^10)/(1-q)]*(1+q^10)(1+q^20)
=S10*3*5
=150