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

  , where f(1)=5  and n>1.

Step-by-step explanation:

The given sequence : 5,-1,-7,-13,-19...

The first term: f(1)=5

We can see that the common difference between each term : d= -6    [-1-5=-6, -7-(-1)=-6, ...]

It mean its arithmetic sequence .

Recursive formula for arithmetic sequence :

Put d= -6 , we get

i.e. Recursive formula can be used to generate the given sequence:

  , where f(1)=5  and n>1.

if its the edgenuty its a for sure ¡

Step-by-step explanation:

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

 -6   -6  -6   -6     the difference between the numbers is -6

 ; where a₁ is the first term, d is the difference, and n is the term

f(1) = 5

      = 11 - 6

       = 5

 TRUE

5

Step-by-step explanation:

, where and

Step-by-step explanation:

The terms of the sequence are:

The first term of this sequence is .

There is a constant difference among the terms.

This constant difference can determined by subtracting a previous term from a subsequent term.

The general term of this arithmetic sequence is given  recursively by

We substitute the necessary values to obtain:

Or

, where and

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

c

Step-by-step explanation:

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

Step-by-step explanation:

Assume your sequence is

5, –1, –7, –13, –19, …  

A recursive formula defines each term of a sequence using the preceding term.

For your sequence,

f(1)  =   5

f(2) =  -1

f(3) =  -7

f(4) = -13

f(5) = -19

We see that

f(2) - f(1)   =   -1 -   5   = -6

f(3) - f(2)  =  -7 -  (-1)  = -6

f(4) - f(3)  = -13 -  (-7) = -6

f(5) - f(4)  = -19 - (-13) = -6

Each term is six units less than the preceding term.

The repeating pattern (recursive formula) is

f(n + 1) - f(n) - 6  or

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

 

Remark

Start with the ones that are wrong because they are in the wrong order.

To find F(n + 1) in a recursive formula, it must be by itself on the left. That makes B wrong.

Find out the difference in the sequence

You are subtracting 6 from the current term to get to the next term. There is no multiplication anywhere. That makes D wrong.

Now to distinguish A and C, you have to decide between addition and subtraction

You are subtracting 6 from the current term to get to the next one.

C

Step-by-step explanation:

the sequence of numbers decrease by 6 each time, so we can write:

f(1) = 5

f(2) = -1

f(3) = -7

f(1) - f(2) = 6

or:

f(2) = f(1) - 6

which means:

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