it is a sequence where f(1)=5 and the constant ratio between terms is "-2"

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

a_n = 11 - 6n

Step-by-step explanation:

you can observe every next element is smaller then the previous one by 6  

a_n = 5 - 6*(n-1)

a_n = 5 - 6n + 6

a_n = 11 - 6n

a_n = 11 - 6n

Step-by-step explanation:

you can observe every next element is smaller then the previous one by 6  

a_n = 5 - 6*(n-1)

a_n = 5 - 6n + 6

a_n = 11 - 6n

The given sequence is

5,–1, –7, –13, –19, ...

And here each current term is the sum of previous term  and -6. That is

It means

current term is the difference of previous term and 6, so we will get

Therefore the correct option is the third option .

The given sequence is

5,–1, –7, –13, –19, ...

And here each current term is the sum of previous term  and -6. That is

It means

current term is the difference of previous term and 6, so we will get

Therefore the correct option is the third option .

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 <<<<< Answer

, 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

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