The formula for a geometric series is Sn=a[(1-r^n)/(1-r)]

Given that:

S4=10S2

S3=26

r>1 (This is only important to avo1d division by zero)

Solution:

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.

Next:

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.

Next:

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:

8r^2-5r+8=0

Which has no real solution thus your problem is impossible