Question

A geometric progression (GP) is such that the 3rd term is 9 times the first, and the second term is one twenty-fourth of the 5th term. Find its 4th term.

A) 3
B) 9
C) 1/3
D) 27

Answer 1

The fourth term of the geometric progression is 27.

Step-by-step explanation:

Let's assume that the first term of the geometric progression (GP) is 'a' and the common ratio is 'r'.

According to the given information, the third term is 9 times the first:

a * r^2 = 9a

r^2 = 9

r = ±3

Since the common ratio of a GP cannot be negative, we take r = 3.

Now, we know that the second term is one twenty-fourth of the fifth term:

a * r = a * 3 = (a * r^4) / 24

3 = r^3 / 24

r^3 = 3 * 24

r^3 = 72

Now, we can find the value of 'a' by substituting 'r' into the first equation:

a * 3^2 = 9a

9 = 9a

a = 1

Now that we know 'a' and 'r', we can find the fourth term:

a * r^3 = 1 * 3^3

a * r^3 = 27

Therefore, the fourth term of the geometric progression is 27. So, the answer is (D) 27.