![]() The recursive formula for a sequence allows you to find the value of the n th term in the sequence if you know the value of the (n-1) th term in the sequence.Ī sequence is an ordered list of numbers or objects. and are often referred to as positive integers. The natural numbers are the numbers in the list 1, 2, 3. The natural numbers are the counting numbers and consist of all positive, whole numbers. The index of a term in a sequence is the term’s “place” in the sequence. Geometric sequences are also known as geometric progressions. For example in the sequence 2, 6, 18, 54., the common ratio is 3.Įxplicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms.Ī geometric sequence is a sequence with a constant ratio between successive terms. For example: In the sequence 5, 8, 11, 14., the common difference is "3".Įvery geometric sequence has a common ratio, or a constant ratio between consecutive terms. Arithmetic sequences are also known are arithmetic progressions.Įvery arithmetic sequence has a common or constant difference between consecutive terms. How much will you have left to pay on the camcorder at the beginning of the twelfth month?Ģ1 Write a recursive rule for the total amount of money paid on the camcorder at the beginning of the nth month.Ģ2 How much will you have left to pay on the camcorder at the beginning of the twelfth month?Īt the beginning of the twelfth month, you would still own $75.\)Īn arithmetic sequence has a common difference between each two consecutive terms. Write a recursive rule for the total amount of money paid on the camcorder at the beginning of the nth month. ![]() Formulas used with arithmetic sequences and. + ( a1 + ( n - 1) d) An arithmetic series is the adding together of the terms of an arithmetic sequence. Arithmetic Series: Sn a1 + ( a1 + d) + ( a1 + 2 d) + ( a1 + 3 d) +. How close to the front can they sit? The class can sit in the 11th row.Ģ0 Suppose you buy a $500 camcorder on layaway by making a down payment of $150 and then paying $25 per month. We will be working with finite sums (the sum of a specific number of terms). Thirty-five students from a class want to sit in the same row. How close to the front can they sit?ġ8 Write the sequence as an explicit rule modeling the number of seats in the nth role.ġst row has 25 seats fixed difference from one row to the next is one additional seat (front to back)ġ9 Thirty-five students from a class want to sit in the same row Write the sequence as an explicit rule modeling the number of seats in the nth role. Evaluate the sequence for the given nth term.ġ7 The first row of a concert hall has 25 seats, and each row after the first has one more seat than the row before it. Grieser Formula Summary: Sequences Explicit Recursive Arithmetic a n a 1 + (n 1)d a n a n-1 + d Geometric a n a 1 rn 1 a n a n-1 r Series Sum of first n integers: i n i 1 2 (n 1) Sum of first n2 integers: i n i 1 2 6 ( )(2n 1 ) Sum of arithmetic series: S. Rewrite the sequence as an explicit and recursive rule. Algebra 2 AII.2 Geometric Sequences and Series Notes Mrs. Evaluate the sequence for the 9th term in the sequence. Then write a rule for the nth term of the sequence for each “YES” example below. Only watch a portion of this video (0:00 – 4:20) review/v/arithmetic-sequencesĭecide whether each sequence is arithmetic.ĩ Sage & scribe activity Turn to your partner and explain the reasoning to each answer. Can you construct linear function that models the information from the first solution? The functions should allow you to find the nth term of the sequence.Ħ How to define an explicit and recursive formula for an arithmetic sequence What is the difference between any two consecutive terms in the first and second solution? Describe the difference in the mathematical approach used to find the solution of each question. ![]() How much will you be earning in the 8th year? How much will you earn over the 8-year period?Ĥ How much will you be earning in the 8th year? You anticipate receiving a $1500 raise each year for the next 7 years. F-IF.A.3: I recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.ģ exploration You have been offered a job paying $28,000 in the first year. ![]() F-BF.A.2: I can construct linear functions given a description of a relationship or two input-output pairs. 4: I can rearrange formulas to highlight a quantity of interestĪ-CED.4: I can rearrange formulas to highlight a quantity of interest. Presentation on theme: "arithmetic sequences & explicit and Recursive formulas unit 1 day 16"- Presentation transcript:ġ arithmetic sequences & explicit and Recursive formulas unit 1 day 16Ģ A-CED. ![]()
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