Answer:
Geometric sequence = ⁵/9, ⁵/3, 5, 15, 45. . .
Arithmetic sequence = 16, 11, 6, 1, -4 . . .
Step-by-step explanation:
A geometric sequence is a sequence of numbers, in which every number in the sequence after the first term is multiplied by a common ratio, which gives us the next term. The common ratio is the ratio of a term to the term before it.
On the other hand, an arithmetic sequence is a sequence of number have a common difference between each consecutive terms. This common difference is gotten by subtracting a term from the term before it.
Now let's examine each sequence given:
==>16, 11, 6, 1, -4 . . .
11 - 16 = -5
6 - 11 = -5
1 - 6 = -5
-4 - 1 = -5
This is an arithmetic sequence. The commons difference "-5" is the same
==>⁵/9, ⁵/3, 5, 15, 45. . .
⁵/3 ÷ ⁵/9 = ⁵/3 × ⁹/5 = ⁹/3 = 3
5 ÷ ⁵/3 = ⁵ × ⅗ = 3
15 ÷ 5 = 3
45 ÷ 15 = 3
The common ratio "3" is the same. This is a geometric sequence.
