Question

Find GP if S6:S3=126:1 and T4=125

Answer 1

S6/S3 = 126/1

=> [a(r^6 - 1)/(r - 1)]/[a(r^3 - 1)/(r - 1)] = 126/1

=> (r^6 - 1) / (r^3 - 1) = 126

=> ((r^3)^2 - 1)/(r^3 - 1) = 126

=> (r^3 + 1) = 126

=> r^3 = 125

=> r = +5 , -5

and T4 = 125

=> a.r^4-1 = 125

=> a.r^3 = 125

=> a.(-125) = 125 or a.(125) = 125

=> a = -1 and a = 1

so, GP is 1,5,25,125...... and -1,-5,-25,-125....