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vladimir1956 [14]
3 years ago
10

Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) =

18
Mathematics
2 answers:
Ad libitum [116K]3 years ago
7 0

Answer:

The recursive formula defines the sequence is f(n)=f(n-1)+2.

Step-by-step explanation:

Three terms of an arithmetic sequence are

f(1) = 6

f(4) = 12

f(7) = 18

It means first term is 6, fourth term is 12 and seventh term is 18.

The formula for nth term of an arithmetic sequence is

a_n=a+(n-1)d

where n is number of term, a is first term and d is common difference.

4th term of the AP is

a_n=6+(4-1)d

12=6+3d                  [\because a_4=f(4)=12]

Subtract 6 from both sides.

12-6=3d

6=3d

Divide both sides by 3.

2=d

The common difference is 2.

The recursive formula for an AP is

a_n=a_{n-1}+d

Substitute d=2 in the above equation.

a_n=a_{n-1}+2

It can be written as

f(n)=f(n-1)+2

Therefore the recursive formula defines the sequence is f(n)=f(n-1)+2.

Nikitich [7]3 years ago
4 0
F(n) = 2(n+2)

can also be written as
f(n) = 2n + 4
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Step-by-step explanation:

You need to use trigonometric stuff here. Since you're given the hypotenuse and an angle you can plug that right into an equation.

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Now that you know the opposite side (DC) you can use tan, too, but I'm going to use cos.

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6 0
3 years ago
Correct function combinations to x2-7x-18
Natasha_Volkova [10]

The factors of the function after factorization f(x)=x^{2} -7x-18 is (x+2) and (x-9)

Given Function  f(x)=x^{2} -7x-18 and we have to find the factors of the given function.

The function whose factors are to be found is   f(x)=x^{2} -7x-18

Factorization means finding various expressions which when together multiplied will give the  function itself. Correct combination can only be found by finding the factors of the function. Without finding factors no one can find the solution of an equation or expression also.

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Learn more about factorization at brainly.com/question/25829061

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