Answer:
Sequence: ordered list of numbers
Series: sum of the terms of a sequence
Arithmetic sequence: the difference between the terms is constant
Geometric Sequence: the ratio between the terms is constant
Step-by-step explanation:
The difference between a series and a sequence is that a sequence is a list of numbers that follow a pattern or rule.
For example
1, 3, 5, 7, 9...
[tex]a_n = 1 +2(n-1)[/tex]
On the other hand, a series is the sum of the terms of a sequence.
1 + 3 + 5 + 7 + 9 + ...+ n
[tex]\sum_{n=1}1 +2 (n-1)[/tex]
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The difference between an arithmetic sequence and a geometric sequence is that:
for the arithmetic sequences the subtraction of:
[tex]a_n - a_{n-1} = d[/tex]
Where d is a constant called difference..
In the Arithmetic sequence the difference between the terms is constant
For the geometric sequences, it is satisfied that the quotient between two consecutive terms is:
[tex]\frac{a_{n-1}}{a_n} = r[/tex]
Where r is a constant value called common ratio
In geometric Sequence the ratio between the terms is constant
