Question

已知等差数列{an}的前n项和为Sn，且S4/S8=1/3,则S8/S16等于_

Answer 1

S4/S8=1/3
s4/(s4+4d*4+a1+a2+a3+a4)=1/3
s4/(s4+4d*4+a1+a2+a3+a4)=1/3
s4/(s4+4d*4+s4)=1/3
s4/(2s4+16d)=1/3
3s4=2s4+16d
s4=16d

s4/s8=1/3
s8=3s4
s8=48d

s16=s8+8d*8+s8
s16=2s8+64d
s16=2*48d+64d
s16=160d

s8/s16=48d/160d=3/10

Answer 2

S4=4a1+4*3*d/2=4a1+6d
S8=S4+4a5+6d
S8=3S4 4a5+6d=2S4
4(a5-a1)=4a1+6d
4*4d=4a1+6d
10d=4a1 d=2a1/5
S8=8a1+8*7*d/2=8a1+28d=8a1+56a1/5=96a1/5
S16=16a1+16*15*d/2=16a1+120d=16a1+48a1=64a1
S8/S16=(96a1/5)/64a1=3/10