Answer :
To find the constant ratio between consecutive terms in a sequence, we use the formula for a geometric sequence, which is characterized by each term being the product of the previous term and a constant ratio, often denoted as [tex]r[/tex].
Let's find the constant ratio for each sequence given in the question:
a. Sequence: 20; -200; 2000; -20000
Find the ratio [tex]r[/tex] between the first term (20) and the second term (-200):
[tex]r = \frac{-200}{20} = -10[/tex]To confirm, check the ratio between the second and third terms (-200 and 2000):
[tex]r = \frac{2000}{-200} = -10[/tex]Check the ratio between the third and fourth terms (2000 and -20000):
[tex]r = \frac{-20000}{2000} = -10[/tex]
The constant ratio for sequence a is [tex]-10[/tex].
b. Sequence: 17; 34; 68; 136
Find the ratio [tex]r[/tex] between the first term (17) and the second term (34):
[tex]r = \frac{34}{17} = 2[/tex]To confirm, check the ratio between the second and third terms (34 and 68):
[tex]r = \frac{68}{34} = 2[/tex]Check the ratio between the third and fourth terms (68 and 136):
[tex]r = \frac{136}{68} = 2[/tex]
The constant ratio for sequence b is [tex]2[/tex].
So, the constant ratio is [tex]-10[/tex] for the sequence a and [tex]2[/tex] for the sequence b.
