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Explicit formulas for arithmetic sequences

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Sal finds explicit formulas of arithmetic sequences given the first few terms of those sequences. He also explores equivalent forms of such formulas.

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1. Arithmetic because the sequence is adding -9 each time.

2. To find the next term you would add -9.

3. The recursive formula would be f(n) = f(n-1) + -9, f(0) =-8

4.To find the nth term, plug any x value into (-8) + -9 (n - 1)

5. The explicit formula would be f( n) = (-8) + -9 (n - 1). To find the explicit rule you can use the formula F(n) = f(1) + d (n-1). (Shown in the picture below)

6. This graph would have a straight line because when the sequence is arithmetic, the line will be linear.

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https://create.kahoot.it/?_ga=1.188546280.1996556836.1452267967&deviceId=0c97523c-a222-43df-9c9e-668b0baf1cc2#user/ad3fe1a6-ee00-45cd-9f46-b2ea23636481/kahoots/created

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A linear graph is used when a sequence is arithmetic and is a straight line.

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An exponential graph is used when a sequence is geometric.

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An explicit formula allows you to find out how much of something there is in a stage by plugging in any given stage to an equation.

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Recursive formula is a formula that is used to determine the next term of a sequence using one or more of the preceding terms.

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A sequence made by multiplying by some value each time.

Example: 2, 4, 8, 16, 32, 64, 128, 256, ...
(each number is 2 times the number before it) The constant ratio is 2.

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Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ...
(each number is 3 larger than the number before it)

The common difference is 3.

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A sequence made by adding or subtracting a value each time