Question

If b1 b2 b3 (b1>0) are three successive terms of a g.p with common ratio r,the value of r for which the inequality b3>4b2-3b1 holds is given by

Answer 1

We are given that b1, b2, b3 are three consecutive terms of a GP.
Let us assume that the terms are
a,ar²,ar³ respectively
Now, put the values of each term in the given inequality
b3>4b2-3b1
=> ar²>4ar-3a
Divide by a
r²>4r-3
Solve for the r
You'll get
r<1 and r>3