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n          |         F(n)

0          |          2

1          |          4

2          |          8

3          |          16

Is exponential because it has a common ratio of 2

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To get this explicit equation you must find how to get from x to y. The explicit equation for the model above is,

f(n)= 2^n+1

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To find the recursive equation you need to find the first difference between two y values. In this model the recursive equation is, f(0)=2

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

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Has a common ratio

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f(n)=-4n+1

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f(1)=-3   f(n)=f(n-1)-4

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1   |   -3

2   |   -7

3   |   -11

4   |   -15

5   |   -19

this table is linear because the first difference is constant, it subtracts 4 every time.

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Has a constant 1st difference

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f(n)=n^2-4
In order to find the explicit, you have to find the difference between f(n) and f(n-1).

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f(1)=-3
f(n)=f(n-1)+2n-1
First, you have to find f(1). Then, you have to find how to get from f(n-1) to f(1)

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n | f(n)
1 | -3
2 | 0
3 | 5
4 | 12
5 | 21

Is quadratic because it has a constant 2nd difference of 7

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Has a constant 2nd difference

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This video covers how to write quadratic equations in recursive form, and gives a few examples .

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How to write quadratic recursive equations.