請問:一遞增的正整數數列<An>滿足An+2(第n+2項)=An(第n項)+An+1(第n+1項)，n為正整數，若A7=120，則A8=?

Sol
A(1)=P，A(2)=Q
A(3)=A(1)+A(2)=P+Q
A(4)=A(2)+A(3)=P+2Q
A(5)=A(3)+A(4)=2P+3Q
A(6)=A(4)+A(5)=3P+5Q
A(7)=A(5)+A(6)=5P+8Q
A(8)=8P+13Q
5P+8Q=120
5｜Q
(1) Q=5
P=16
A(1)>A(2) (不合)
(2) Q=10
P=8
A(8)=64+130=194………………
(3) Q=15
P=0 (不合)
So
A(8)=194