Arithmetic progression's first n terms and formulas, as well as angular coordinates and properties should be used.

If * * * has 2n terms,

S2n=2n[a 1+a(2n)]/2

∫ 1+2n = n+(n+ 1)

∴a 1+a(2n)=an+a(n+ 1)

∴s2n=n(an+a(n+ 1))；

∫S couple =[a2+a(2n)]*n/2,

S odd number = [a1+a (2n-1)] * n/2.

a2+a(2n)=2a(n+ 1)

a 1+a(2n- 1)=2an

∴S even /S odd = a (n+1)/an;

If * * * has 2n+ 1,

s(2n+ 1)=[a 1+a(2n+ 1)]*(2n+ 1)/2

∫ 1+2n+ 1 =(n+ 1)+(n+ 1)

∴∴a 1+a(2n+ 1)=2a(n+ 1)

∴s(2n+ 1)=(2n+ 1)*a(n+ 1)；

S even number =[a2+a(2n)]*n/2

S odd number = {a1+a (2n+1)] * (n+1)/2

∫2+2n = 1+(2n+ 1)= 2(n+ 1)

∴a2+a(2n)=a 1+a(2n+ 1)=2a(n+ 1)

∴S couple =[a2+a(2n)]*n/2=na(n+ 1)

S odd = {a1+a (2n+1)] * (n+1)/2 = (n+1) a (n+1).

∴S even -s odd =-a (n+1); S even /S odd =n/(n+ 1)