Question

Find the two possible value of n if n-3, 3n+5 and 18n-5 are three consecutive term of a geometric progression (Gp)

A. n = 5 and n = 7
B. n = 2 and n = 4
C. n = 3 and n = 6
D. n = 1 and n = 2

Answer 1

By using the property of a geometric progression that the square of the middle term equals the product of the other two terms, a quadratic equation is formed. Solving this equation gives the possible values of n as 1 and 2, corresponding to option D.

Step-by-step explanation:

To find the two possible values of n for which n-3, 3n+5, and 18n-5 form a geometric progression (GP), we can use the property of GP that the square of the middle term is equal to the product of the other two terms. This gives us the equation:

(3n + 5)2 = (n - 3)(18n - 5).

Expanding and simplifying the equation, we get:

9n2 + 30n + 25 = 18n2 - 5n - 54n + 15,

which simplifies further to:

0 = 9n2 - 89n - 10.

This is a quadratic equation that can be solved by factoring or using the quadratic formula. The solutions to this equation give the possible values of n. After solving, we find n = 1 and n = 2 as the two possible values, which corresponds to option D.