Question

已知等比数列{a n }中，公比q＞0，且a 1 +a 4 =9，a 2 a 3 =8，则 a 2012 + a 2013 a

已知等比数列{a n }中，公比q＞0，且a 1 +a 4 =9，a 2 a 3 =8，则 a 2012 + a 2013 a 2010 + a 2011 =______．

Answer 1

由等比数列的性质可知，a
2
a
3
=a
1
a
4
=8
∵a
1
+a
4
=9
∴
a
1
=1
a
4
=8
q=2
或
a
1
=8
a
4
=1
q=
1
2
∴q
2
=
a
2012
+
a
2013
a
2010
+
a
2011
=4 或
1
4
故答案为：4或
1
4