第2个回答 2021-09-12
已知正等比数列,且S2=6, S4=30,求S6.
等比数列和公式Sn=a1(1-q^n)/(1-q)
S2=a1(1-q^2)/(1-q)=6
S4=a1(1-q^4)/(1-q)=30
S4÷S2=[a1(1-q^4)/(1-q)]÷[a1(1-q^2)/(1-q)]=30÷6
化简后可得(1-q^4)÷(1-q^2)=5即(1+q^2)=5
求出q=2或-2
由于已知此数列是正等比数列,所以q=2
S6=a1(1-q^6)/(1-q)=30
S6÷S4=[a1(1-q^6)/(1-q)]÷[a1(1-q^4)/(1-q)]=(1-q^6)÷(1-q^4)=(1-2^6)÷(1-2^4)=4.2
S6=4.2×S4=4.2×30=126