Explain and compare sequences that have first differences, second differences, and third differences and the type of relationship they satisfy.

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Explain and compare sequences that have first differences, second differences, and third differences and the type of relationship they satisfy

When a sequence has first difference, that mean it has the same difference between the number through out. Such a sequence is Linear. Examples of such are :

1, 3, 5, 7, 9,

2, 5, 8, 11,

When a sequence has second difference, that mean it does not have the same difference between the number through out. It has the same sequence at the second order.

Such a sequence is quadratic. Example of such is :

1, 3, 6, 10, 15,

When a sequence has third difference, that means it does not have the same difference between the number through out in the first and second order but in the third order. Such a sequence is exponential. Example of such is :

1, 2, 5, 10, 17,

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