# 10 6 14 Recursive Formulas For Arithmetic Sequences

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10 -6 -14 Recursive Formulas For Arithmetic Sequences

Do you know the definition of “recursive”? 11/30/2020 According to Merriam Webster: relating to a procedure that can repeat itself indefinitely

10 -6 -14 Mathematically Speaking Recursive Formula: – Formula where each term is based on the term before it. Arithmetic Sequence: – Sequence with a constant difference between terms.

Domain of arithmetic sequences You can use arithmetic sequences as linear functions to model realworld situations. While the domain of some linear functions is the set of all real numbers, the domain of an arithmetic sequence as a linear function is the set of counting numbers, {1, 2, 3, 4, …}.

Example • 11/30/2020 Consider the sequence generated by 2000, 2040, 2080, 2120, 2160, . . . • Describe this sequence in words. n = positive integers ≥ 2

How is a recursive function represented? 1 -6 -14

10/6/14 YOU TRY: Write an arithmetic sequence for the range of this sequence, If you buy a new car, you might be advised to have an oil change after driving 1000 miles and every 3000 miles thereafter. Then the following sequence gives the mileage when oil changes are required: 1000 4000 7000 10000 13000 16000 n = positive integers ≥ 2

Another example; This time write the recursive formula • Briana borrowed \$870 from her parents for airfare to Europe. She will pay them back at the rate of \$60. 00 per month. Let an be the amount she still owes after n months. Find a recursive formula for this sequence. n = positive integers ≥ 2

Graph of an Arith. Seq. • Discrete Domain and Range • Constant Increase or Decrease • Your first input is 1, not 0

11/30/2020 3 -8 Explicit Formulas For Arithmetic Sequences

11/30/2020 Arithmetic Sequences Explicit Formula – Formula where any term can be found by substituting the number of that term. – We can develop an explicit formula for an Arithmetic Sequence from the recursive formula

Explicit Formula n 1 2 3 4 an 1000+3000=4000+3000=7000+3000=10000 11/30/2020 d 3000

11/30/2020 • So, for our oil change example, the explicit formula looks like:

Examples 10/22/13 1. Find the 40 th term of the arithmetic sequence 100, 97, 94, 91, …. . 2. In a concert hall the 1 st row has 20 seats in it, and each subsequent row has 2 more seats than the row in front of it. If the last row has 64 seats, how many rows are in the concert hall? 3. Answer 23 rows!