Answer:
The given sequence 6, 7, 13, 20, ... is a recursive sequence
Step-by-step explanation:
As the given sequence is
[tex]6, 7, 13, 20, ...[/tex]
- It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.
As
[tex]d = 7-6=1[/tex], [tex]d = 13-7=6[/tex]
As d is not same. Hence, it cannot be an arithmetic sequence.
- It also cannot be a geometrical sequence and exponential sequence.
It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.
As
[tex]r = 7-6=1[/tex], [tex]r = 13-7=6[/tex]
[tex]r = \frac{7}{6}[/tex], [tex]r = \frac{13}{7}[/tex]
As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.
So, if we carefully observe, we can determine that:
- The given sequence 6, 7, 13, 20, ... is a recursive sequence.
Please have a close look that each term is being created by adding the preceding two terms.
For example, the sequence is generated by starting from 1.
[tex]{\displaystyle F_{1}=1[/tex]
and
[tex]{\displaystyle F_{n}=F_{n-1}+F_{n-2}}[/tex]
for n > 1.
Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence
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