Given, The sum of the first 8 terms of a GP is 5 times the sum of its first 4 terms. The formula for the sum of the first n terms of a GP is: Sn=a
1−rn
1−r
Substitute for S8 and S4 into the equation: a
1−r8
1−r
=5×a
1−r4
1−r
1−r8
1−r4
=5 r8−5r4+4=0 Let x=r4, giving the quadratic equation: x2−5x+4=0 Solving for x , we get: x=4 or x=1 Since x=r4, this gives: r4=4⇒r=±√2 The number of possible real values of r is two: ±√2.