The formula for a geometric series is Sn=a[(1-r^n)/(1-r)]
r>1 (This is only important to avo1d division by zero)
Since, S4=10S2 we have:
a[(1-r^4)/(1-r)]=10[(1-r^2)/(1-r)] multiply by (1-r):
a[(1-r^4)]=10[(1-r^2)] Factor (1-r^4):
a[(1-r^2)(1+r^2)]=10[(1-r^2)] divide by (1-r^2):
a(1+r^2)=10 THIS IS YOUR FIRST EQUATION.
Since S3=26 we have:
a[(1-r^3)/(1-r)]=26 Long divide 1-r^3 by 1-r to get:
a(1+r+r^2)=26 THIS IS YOUR SECOND EQUATION.
Divide the first equation by the second:
(1+r^2)/(1+r+r^2)=10/26 or 5/13. Cross Multiply:
13+13r^2=5+5r+5r^2 Collect Terms:
Which has no real solution thus your problem is impossible