问题 解答题

已知a1,a2,a3,a4成等比数列,且a1=a2+36,a3=a4+4,求a1,a2,a3,a4

答案

设公比是q,则a2=a1•q,a3=a1•q2,a4=a1•q3

∴a1-a2=a1-a1•q=a1(1-q)=36  ①

a3-a4=a1•q2-a1•q3=a1•q2•(1-q)=4  ②

=q2=
1
9

解得:q=±

1
3

(1)当q=

1
3
时,(1-
1
3
)a1=36  解得:a1=54,则a2=18,a3=6,a4=2

(2)当q=-

1
3
时,[1-(-
1
3
)]a1=36,解得a1=27,则a2=-9,a3=3,a4=-1

终上所述:

a1,a2,a3,a4的值为:a1=54,a2=18,a3=6,a4=2

                  或:a1=27,a2=-8,a3=3,a4=-1

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