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Dmitriy789 [7]
3 years ago
14

Given the formula for an arithmetic sequence f(7) = f(6) + 4 written using a recursive formula, write the sequence using an arit

hmetic formula
Of(7) = f(1) + 24

1(7) = f(1) + 20

Of(7) = f(1) + 12

Of(7) = f(1) + 4
Mathematics
2 answers:
natita [175]3 years ago
6 0

Answer:

Of(7) = f(1) + 24

Step-by-step explanation:

Since this Arithmetic Sequence can be written recursively as a function, then we can write the whole sequence, by adding the common difference to the previous function. So writing it as an Arithmetic formula is (placing an example, with a common difference of 4 units):

\left.\begin{matrix}n &1&2&3&4&5&6 &7\\f(n)&2&6&10 & 14&18&22&26 \end{matrix}\right|\\f(n)=f(n-1)+d\:\: (Recursive \: Formula)\Rightarrow a_{n}=a_{n-1}+4\: \: \: (Arithmetic\: Formula)\\Of(7)=f(1)+6*4\Rightarrow a_{7}=a_{1}+(7-1)4\Rightarrow a_{7}=a_{1}+24\\

kap26 [50]3 years ago
5 0

Answer:

f(7) = f(1) + 24

Step-by-step explanation:

Arithmetic explicit formula has the form:

f(n) = f(1) + (n-1)*d

Arithmetic recursive formula has the form:

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

Given the expression: f(7) = f(6) + 4, it can be seen it's expressed in the recursive form with n = 7, n-1 = 6 and d = 4. Using these values in the explicit formula we get:

f(7) = f(1) + 6*4

f(7) = f(1) + 24

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Which ofnthe following shows the correct use of distributive property when solving 1/3(33-x)=135,2
madam [21]

Answer: OPTION C.

Step-by-step explanation:

The missing options are:

A. (33 - x) = \frac{1}{3} * 135.2\\\\B. (\frac{1}{3} *33) - \frac{1}{3} x = \frac{1}{3} * 135.2\\\\C.(\frac{1}{3}  * 33) - \frac{1}{3} x = 135.2\\\\D. (\frac{1}{3}  * 33) + \frac{1}{3} x = 135.2

In order to solve this exercise you need to remember the following:

1. The Distributive property states that:

a(b+c)=ab+ac\\\\a(b-c)=ab-ac

2. The multiplication of signs:

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In this case the exercise gives you the following equation:

\frac{1}{3}(33-x)=135.2

Since you need to solve for the variable "x" in order to  find its value, the first  step you must apply in the in the procedure is to eliminate the parentheses applying the Distributive property.

Then, you must multiply everyting inside the parentheses by \frac{1}{3}.

Therefore,based on the explanation, you know that the correct use of the Distributive property is:

\frac{1}{3}*33-\frac{1}{3}x=135.2

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