Mathematics, 20.12.2019 06:31 katelynamber10

10. you are given the first four terms of an arithmetic sequence. why might you

use a recursive formula? why might you use an explicit formula? under what

conditions might a recursive formula be preferred over the explicit formula?

under what conditions might an explicit formula be preferred over the

recursive formula?

Answers: 3

Show answers

Answers

Answer from: ayoismeisalex

1)It might be more convenient to write some Arithmetic Sequences as functions.

2) Whenever I need to find out any term of a given Sequence, as long as I know which value is for "n"

3)If it is known the previous term of a Sequence you might prefer it over the explicit one.

Step-by-step explanation:

1) Why might you use a recursive formula?

It might be more convenient to write some Arithmetic Sequences as functions. Since you know the previous term.

Imagine we just have (...,4,... from an Arithmetic Sequence whose common difference is 5.

Example:

$\left\{\begin{matrix}f(1)=4\\f(n)=f(n-1)+5\end{matrix}\right. \Rightarrow f(2)= f(1)+5 \Rightarrow f(2)=4+5 \Rightarrow f(2)=9$

2) Why might you use an explicit formula?

Whenever I need to find out any term of a given Sequence, as long as I know which value is for "n"

For the same Sequence, let's use the explicit one:

$a_{n}=4+5(n-1) \Rightarrow a_{6}=4+5(5)\Rightarrow a_{6}=29$

3) Under what conditions might a recursive formula be preferred over the explicit formula?

If it is known the previous term of a Sequence you might prefer it over the explicit one.

Answer from: Quest

add the table and i will answer correctly

step-by-step explanation:

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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