2, 4, 6, 10, ... is an example of a recursive sequence
Step-by-step explanation:
The recursive sequence is a sequence in which terms are defined using one or more previous terms which are given
The recursive formula of the nth term of the arithmetic sequence is:
- [tex]a_{1}[/tex] = first term; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d, where d is the common difference between each two consecutive terms
- While it can be defined with a recursive formula, it is not a recursive sequence.
The recursive formula of the nth term of the arithmetic sequence is:
- [tex]a_{1}[/tex]= first term; [tex]a_{n}[/tex] = r • [tex]a_{n-1}[/tex] , where r is the common ratio between each two consecutive terms
- While it can be defined with a recursive formula, it is not a recursive sequence.
In 1, 3, 9, 27, ............
∵ 3 ÷ 1 = 3
∵ 9 ÷ 3 = 3
∵ 27 ÷ 3 = 3
∴ There is a constant ratio between each to consecutive terms
∴ 1, 3, 9, 27, ..... represents a geometric sequence
Let us write its recursive formula
∵ [tex]a_{1}[/tex] = 1 and r = 3
∴ [tex]a_{1}[/tex] = 1; [tex]a_{n}[/tex] = 3 • [tex]a_{n-1}[/tex]
- while it can be defined with a recursive formula, it is not a
recursive sequence.
1, 3, 9, 27, ..... is not an example of a recursive sequence
In 2, 4, 6, 10
∵ 2 + 4 = 6
∵ 4 + 6 = 10
- That means the third term is the sum of the first two
previous terms and the fourth term is the sum of the
two previous terms of it
∴ [tex]a_{n}=a_{n-1}+a_{n-2}[/tex]
- The recursive sequence is a sequence in which terms are
defined using one or more previous terms which are given
∴ 2, 4, 6, 10, ... is a recursive sequence
2, 4, 6, 10, ... is an example of a recursive sequence
In 2, 5, 8, 11, ...
∵ 5 - 2 = 3
∵ 8 - 5 = 3
∵ 11 - 8 = 3
∴ There is a common difference between each to consecutive terms
∴ 2, 5, 8, 11, ... represents an arithmetic sequence
Let us write its recursive formula
∵ [tex]a_{1}[/tex] = 2 and d = 3
∴ [tex]a_{1}[/tex] = 2; [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3
- while it can be defined with a recursive formula, it is not a
recursive sequence.
2, 5, 8, 11, ... is not an example of a recursive sequence
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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