Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

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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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