等差数列{an}中,a1+a2+…+a50=200,a51+a52+…+a100=2700,则a1等于( ) A.-1221 B.-21.5 C.-20.5 D.-20
问题描述:
等差数列{an}中,a1+a2+…+a50=200,a51+a52+…+a100=2700,则a1等于( )
A. -1221
B. -21.5
C. -20.5
D. -20
答
∵a1+a2+…+a50=200 ①
a51+a52+…+a100=2700 ②
②-①得:50×50d=2500,
∴d=1,
∵a1+a2+…+a50=200,
∴na1+
n(n-1)d=200,1 2
∴50a1+25×49=200,
∴a1=-20.5,
故选C.