已知数列{an}是等差数列,an≠0,若2lga2=lga1+lga4,则a7+a8a8+a9的值是()A.1517B.1或1517C.1315D.1或1315-数学

题目简介

已知数列{an}是等差数列,an≠0,若2lga2=lga1+lga4,则a7+a8a8+a9的值是()A.1517B.1或1517C.1315D.1或1315-数学

题目详情

已知数列{an}是等差数列,an≠0,若2lga2=lga1+lga4,则
a7+a8
a8  +a9
的值是(  )
A.
15
17
B.1或
15
17
C.
13
15
D.1或
13
15
题型:单选题难度:偏易来源:不详

答案

∵数列{an}是等差数列,an≠0若2lga2=lga1+lga4,
a22=a1?a4,即(a1+d )2=a1(a1+3d),
化简可得 a1=d,或d=0.
当 a1=d 时,
a7+a8
a8  +a9
=class="stub"15d
17d
=class="stub"15
17

当d=0时,
a7+a8
a8  +a9
=
2a1
2a1
=1.
总上可得,
a7+a8
a8  +a9
=class="stub"15
17
 或1,
故选B.

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