Question

设一列数A1.A2.A3.......A100中任意三个相邻数之和都是37，已知A2=25,A9=2x,A99=3-x,那么A100=？

Answer 1

解：由任意三个相邻数之和都是37可知：
a
1
+a
2
+a
3
=37
a
2
+a
3
+a
4
=37
a
3
+a
4
+a
5
=37
…
a
n
+a
n+1
+a
n+2
=37
可以推出：a
1
=a
4
=a
7
=…=a
3n+1
a
2
=a
5
=a
8
=…=a
3n+2
a
3
=a
6
=a
9
=…=a
3n
∴a
9
=a
99
即：a
9
=a
99
2x=3-x
x=1
∴a
3
=2
∴a
100
=a
1
=37-25-2=10．