Arithmetic Sequence

The interior angles of a convex polygonform an arithmetic sequence with common
difference 4degree. If the largest interior angle of the polygon is 162degree.Find the
number of sides of the polygon.
Sol
設為n邊形
a1=162，d=－4
an=a1+(n－1)*(－4)=166－4n
(n－2)*180=(162+166－4n)*n/2
180n－360=164n－2n^2
2n^2+16n－360=0
n^2+8b－180=0
(n－10)(n+18)=0
n=10or n=－18(不合)