已知等比数列an的公比q

1个回答

  • Sn=a1(q^n-1)/(q-1)

    S10=a1(q^10-1)/(q-1)=3,a1/(q-1)=3/(q^10-1)

    S30=a1(q^30-1)/(q-1)=63

    相除:

    S30/S10=[a1(q^30-1)/(q-1)]/[a1(q^10-1)/(q-1)]=63/3

    (q^30-1)/(q^10-1)=21

    q^20+q^10=20

    q^10=4

    s40-s20=a1(q^40-1)/(q-1)-a1(q^20-1)/(q-1)

    =a1(q^40-q^20)/(q-1)

    =(q^40-q^20)[3/(q^10-1)]

    =3(q^40-q^20)/(q^10-1)

    =3(4^4-4^2)/(4-1)

    =(4^2-1)4^2

    =240