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romanna [79]
3 years ago
9

three terms of an arithmetic sequence are shown. f(1)=3, f(3)=6, f(7)=12 what recursive formula could define the sequence ? A. f

(n+1)=2f(n) B. f(n+1)=f(n)+3 C. f(n+1)=f(n)+1.5 D. F(n+1)=0.5f(n)
Mathematics
1 answer:
WITCHER [35]3 years ago
8 0
an\ arithmetic\ sequence:\\\\ d\ \ \rightarrow\ \ the\ difference\\\\f(n)=f(1)+(n-1)\cdot d\\\\f(n+1)=f(1)+n\cdot d\\\\f(n+1)-f(n)=f(1)+n\cdot d-[f(1)+n\cdot d- d]=\\\\=f(1)+nd-f(1) -nd+d=d\\\\\Rightarrow\ \ \ f(n+1)=f(n)+d

f(1)=3\ \ \ and\ \ \ f(3)=6\\\\f(3)=f(1)+(3-1)\cdot d\ \ \ \Rightarrow\ \ \ 6=3+2d\\\\ \ \ \Rightarrow\ \ \ 2d=3\ \ \ \Rightarrow\ \ \ d=1.5\\\\ f(n+1)=f(n)+d\ \ \ \Rightarrow\ \ \ f(n+1)=f(n)+1.5\\\\\\Ans.\ \ \ f(1)=3\ \ \ and\ \ \ f(n+1)=f(n)+1.5
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Answer:

f(4)=\frac{1}{2}

f(x) = 4 when x is 8

Step-by-step explanation:

Domain is the set of x values that make the function defined. Allowed x values for the function (mapping).

The Range is the set of y values that make the function defined. Allowed y values for the function (mapping).

  • Whenever we need to find f(a), suppose, then we look for "a" in the domain and see its corresponding value mapping in the range.
  • Whenever we will be given a value for f(x) = a, suppose, and we have to find "x", we look at the value a in the range and find corresponding x value in the domain.

Firstly, we need f(4), so we look for "4" in domain and see which number it corresponds to in range.

That is \frac{1}{2}

Thus,

f(4)=\frac{1}{2}

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We want "x" value that gives us a "y" value of 4. We look for "4" in the range and see which value it corresponds to. That is "8". So,

f(8) = 4

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Read more about Triangle proof at; brainly.com/question/1248322

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