Question

等比数列﹛an﹜前5项和为1,前10项和为33,求公比

Answer 1

Sn=a1(1-q^n)/(1-q)

∴S5=a1(1-q^5)/(1-q)=1

S10=a1(1-q^10)/(1-q)=33

S10/S5=(1-q^10)/(1-q^5)=33

(1+q^5)(1-q^5)/(1-q^5)=33

1+q^5=33

∴q=2