请教两个关于等比数列的问题1.{An}是等比函数,且A1+A4=18,A2+A3=12,求S102.{An}是等比函数,且q=2,S5=1,求S10

Question

请教两个关于等比数列的问题
1.{An}是等比函数,且A1+A4=18,A2+A3=12,求S10
2.{An}是等比函数,且q=2,S5=1,求S10

Answer 1

1.
a1+a1*q^3=18(1)
a1*q+a1*q^2=12(2)
(1)÷(2):
(1+q^3)/(q+q^2)=3/2
[(1+q)(1-q+q^2)]/[q(1+q)]=3/2
(1-q+q^2)/q=3/2
2(1-q+q^2)=3q
2-2q+2q^2=3q
2q^2-5q+2=0
(2q-1)(q-2)=0
q=1/2或q=2
q=1/2,a1=16
S10=16*[1-(1/2)^10]/(1-1/2)=1023/32
q=2,a1=2
S10=2*(1-2^10)/(1-2)=2046
2)
S5=a1(1+q+q^2+q^3+q^4)=1
s10-s5=a1(a^5+q^6+q^7+q^8+q^9)=a1q^5(1+q+q^2+q^3+q^4)=s5 2^5=32
s10=s5+32=33