If a ≠ B, and a, x1, X2, B and a, Y1, Y2, Y3, B are arithmetic sequences, then (x1-x2) / (y1-y2)=

If a ≠ B, and a, x1, X2, B and a, Y1, Y2, Y3, B are arithmetic sequences, then (x1-x2) / (y1-y2)=

x(n)=a+nd,
b=x(3)=a+3d,d=(b-a)/3,
x(1)-x(2)=-d=-(b-a)/3,
y(n)=a+nc,
b=y(4)=a+4c,c=(b-a)/4,
y(1)-y(2)=-c=-(b-a)/4,
[x(1)-x(2)]/[y(1)-y(2)] = (1/3)/(1/4) = 4/3

Let a ≠ B, and the sequence a, x1, X2, B and a, Y1, Y2, Y3, Y4, B are arithmetic sequence respectively, then find x2-x1 / y4-y1

x2-x1=（b-a）/3
y4-y1=（b-a）/5
x2-x1 / y4-y1 =5/3

If an + 1 = (2Sn) + 1, then the common ratio q =?

a(n+1)=2Sn+1
Then an = 2S (n-1) + 1
And SN-S (n-1) = an
So a (n + 1) - an = 2An
a(n+1)=3an
So q = 3