Question

Which of the following is an example of a recursive sequence?

Answer 1

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:

• $a_{1}$ = first term;  $a_{n}$ = $a_{n-1}$ + 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:

• $a_{1}$= first term;  $a_{n}$ = r • $a_{n-1}$ ,  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

∵ $a_{1}$ = 1 and r = 3

∴ $a_{1}$ = 1; $a_{n}$ = 3 • $a_{n-1}$

- 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

∴ $a_{n}=a_{n-1}+a_{n-2}$

- 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

∵ $a_{1}$ = 2 and d = 3

∴ $a_{1}$ = 2; $a_{n}$ = $a_{n-1}$ + 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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