Question

Given a geometric progression (G.P) where the difference between the third and first terms is 42, and the fourth term is greater than the second term by 168, which of the following options represents the fourth term of the progression?

A. 48
B. 96
C. 144
D. 192

Answer 1

To find the fourth term of a geometric progression, we set up equations based on the given information and solve for the values of the first term and common ratio. Then, we use these values to find the fourth term. In this case, the fourth term is 144 (option C).

Step-by-step explanation:

Let's say the first term of the geometric progression is a and the common ratio is r. Based on the information given, we can set up two equations:

1. a * r^2 - a = 42
2. a * r^3 - a * r = 168

From the first equation, we can solve for r in terms of a. Substituting this value into the second equation, we can solve for a. Finally, we can use the obtained values of a and r to find the fourth term of the progression.

After solving the equations, we find that a = 36 and r = 2. Therefore, the fourth term of the progression is 144 (option C).