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Match each sequence to its appropriate recursively defined function.

f(1) = -18

f(n) = 6 · f(n - 1) for n = 2, 3, 4, ...

f(1) = -18

f(n) = f(n - 1) + 21 for n = 2, 3, 4, ...

f(1) = 11

f(n) = f(n - 1) + 22 for n = 2, 3, 4, ...

f(1) = 11

f(n) = 3 · f(n - 1) for n = 2, 3, 4, ...

f(1) = -18

f(n) = f(n - 1) + 22 for n = 2, 3, 4, ...

f(1) = -18

f(n) = 2 · f(n - 1) for n = 2, 3, 4, ...

Sequence

Recursively Defined Function

11, 33, 55, 77, ...

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-18, -108, -648, -3,888, ...

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-18, 3, 24, 45, ...

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Respuesta :

sqdancefan

Answer:

  see below

Step-by-step explanation:

Since there are fewer sequences than functions, we'll identify the matchup according to the sequence.

11, 33, 55, 77, ...

The first term is 11. The terms have a common difference of 33 -11 = 22. That is, each term is 22 more than the previous one. The appropriate recursive function is ...

  • f(1) = 11
  • f(n) = f(n-1) +22 for n > 1

__

-18, -108, -648, -3888, ...

The first term is -18. The terms obviously do not have a common difference, but their common ratio is -648/-108 = -108/-18 = 6. That is, each term is 6 times the previous one. Then the appropriate recursive function is ...

  • f(1) = -18
  • f(n) = 6·f(n-1) for n > 1

__

-18, 3, 24, 45, ...

The first term is -18. The terms have a common difference of 3-(-18) = 21. That is, each term is 21 more than the previous one. The appropriate recursive function is ...

  • f(1) = -18
  • f(n) = f(n-1) +21 for n > 1

Answer:

11, 33, 55, 77, ...=f(n) = f(n - 1) + 22 for n = 2, 3, 4, ...

-18, -108, -648, -3,888, ...=f(n) = 6 · f(n - 1) for n = 2, 3, 4, ...

-18, 3, 24, 45, ...=f(n) = f(n - 1) + 21 for n = 2, 3, 4, ...

Step-by-step explanation:

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