Question 10

Explanation

Given quadratic equation

With roots $x_1$ and $x_2$, the product of roots is

So the geometric sequence is $x_1, k, x_2$.

The ratio between terms is

Factorize

Determine the form of the quadratic equation based on the obtained value of $k$.

$k = 4$

Check the discriminant value, the roots are not integers.

$k = -1$

Therefore the sequence is

The ratio between terms is

Then the $n$th term of the sequence is