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The recursive formula [tex]a_n = a_{n-1}-6[/tex] can be used to generate the shown sequence

Step-by-step explanation:

Recursive formula is the formula that is used to generate the next term of a sequence using previous term.

The general form of arithmetic sequence's recursive formula is:

[tex]a_n = a_{n-1}+d[/tex]

Given

5,-1,-7,-13,-19

Here

[tex]a_1 = 5\\a_2 = -1\\a_3 = -7[/tex]

First of all we have to find the common difference of the sequence.

So,

[tex]d = a_2 -a_1 = -1-5 = -6\\d = a_3-a_2 = -7+1 = -6[/tex]

Putting the value of d in the general recursive formula

[tex]a_n = a_{n-1}-6[/tex]

Hence,

The recursive formula [tex]a_n = a_{n-1}-6[/tex] can be used to generate the shown sequence

Keywords: Sequence, arithmetic sequence

Learn more about arithmetic sequence at:

  • brainly.com/question/3375830
  • brainly.com/question/3398261

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tq559

Answer:

C: f(n + 1) = f(n) - 6

Step-by-step explanation:

f(1) = 5

f(2) = -1

f(3) = -7

f(1) - f(2) = 6

or:

f(2) = f(1) - 6

Re-written to:

f(n + 1) = f(n) - 6

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