Question

3. Is this sequence geometric: 1.5, -4.5, 13.5, -40.5? If it is, what are a, and r? [3 pts]

Answer 1

Answer

The sequence is geometric.

a = 1.5

r = -3

Explanation

Given:

The sequence given is: 1.5, -4.5, 13.5, -40.5

What to find:

If the sequence is geometric, also to find a, r.

Solution:

To check if it's geometric, we shall solve the following:

$\frac{-4.5}{1.5}=\frac{13.5}{-4.5}=\frac{-40.5}{13.5}=-3$

This shows that the sequence is geometric.

The first term, a, of the sequence is 1.5.

And the common ratio, r = (second term/first term) = (-4.5/1.5) = -3.

Hence, the sequence is geometric, a = 1.5 and r = -3.