Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?

Answer 1

The recursive formula $a_n = a_{n-1}-6$ 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:

$a_n = a_{n-1}+d$

Given

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

Here

$a_1 = 5\\a_2 = -1\\a_3 = -7$

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

So,

$d = a_2 -a_1 = -1-5 = -6\\d = a_3-a_2 = -7+1 = -6$

Putting the value of d in the general recursive formula

$a_n = a_{n-1}-6$

Hence,

The recursive formula $a_n = a_{n-1}-6$ 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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Answer 2

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