等差数列{an}公差d=3,前50项的和为50.(1)求an.(2)设{an}中三项a1,ak,am构成公比为4的等比数列,求k,m.
问题描述:
等差数列{an}公差d=3,前50项的和为50.(1)求an.(2)设{an}中三项a1,ak,am构成公比为4的等比数列,求k,m.
答
(1)
an=a1+(n-1)3
S50= (2a1+147)25=50
2a1+147=2
a1=-145/2
an=-145/2+ (n-1)3
=3n-(151/2)
ak/a1=4
(3k-(151/2))/(-145/2) =4
3k-(151/2)= -290
k=2
am/ak=4
(3m-(151/2))/(6-151/2)=4
3m-(151/2)=-278
m=4