3-7 Recursive Formulas For Arithmetic Sequences 4/21/2017 3-7 Recursive Formulas For Arithmetic Sequences

4/21/2017 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

Arithmetic Sequences Arithmetic Sequence: Recursive Formula: 4/21/2017 Arithmetic Sequences Arithmetic Sequence: Sequence with a constant difference between terms. Here it was d = 3000 Recursive Formula: Formula where each term is based on the term before it Recursive Formula for an Arithmetic Seq:

4/21/2017 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

Example Consider the sequence generated by 4/21/2017 Example Consider the sequence generated by Describe the sequence in words Write the 1st five terms of the sequence

4/21/2017 Example 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.

Graph of an Arith. Seq. Discrete Domain Constant Increase or Decrease 4/21/2017 Graph of an Arith. Seq. Discrete Domain Constant Increase or Decrease Collinear Points

3-8 Explicit Formulas For Arithmetic Sequences 4/21/2017 3-8 Explicit Formulas For Arithmetic Sequences

Arithmetic Sequences Explicit Formula 4/21/2017 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 4/21/2017 n 1 2 3 4 # of d 1 2 3 an 1000 1 2 3 an 1000 1000+3000=4000 4000+3000=7000 7000+3000=10000

So, for our oil change example, the explicit formula looks like: 4/21/2017 So, for our oil change example, the explicit formula looks like:

4/21/2017 Examples Find the 40th term of the arithmetic sequence 100,97,94,91,….. In a concert hall the 1st 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?