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Alg2 Notes 9.3.notebook April 12, 2013
Skills we need
Skills we've learned
93 Arithmetic Sequences and Series
7. Identify which sequences are linear:5,7,9,11,... 5, 10, 20, 40, ... 5/2, 5/4, 5/8, ...
Warmup Answers
7. Identify which sequences are linear:5,7,9,11,... 5, 10, 20, 40, ... 5/2, 5/4, 5/8, ...
Alg2 Notes 9.3.notebook April 12, 2013
93 Arithmetic Sequences and Series
Find the general rule for arithmetic sequencesFind the indicated terms of an arithmetic sequenceFind the sums of arithmetic series
Predictions of linear patterns
I. Arithmetic. Linear.
You can think of an arithmetic sequence as a linear function with sequential natural numbers as the domain. Recursive Rule for Arithmetic Sequences:
a1 = beginning numberan = an1 + d
General Rule for Arithmetic Sequences: an = a1 + (n 1)d note: clean up
1) Write this sequence recursively and using a general rule (explicit): 3, 6, 9, 12, 15, 18, ...
Linear:y = mx + b
m = d
Alg2 Notes 9.3.notebook April 12, 2013
2) Determine whether each sequence could be arithmetic. If so, find the common first difference, the next term, and write the explicit rule. Then find the 100th term.4, 5, 6, 7, ... 3, 5, 9, 15, 23, ...
II. Finding the Missing Term
3) Find the missing terms in the arithmetic sequence: 17, ___, ___, ___, 7Linear: We know two points: (1, 17) and (5, 7).Find the equation, then find the 2nd, 3rd and 4th term.
Book Method:Step 1: Find the common differenceYou know a1 = 17 and a5 = 7
–7 = 17 + (5 – 1)(d) d = 6
Step 2: Find the missing terms using d = 6 and a1 = 17
Alg2 Notes 9.3.notebook April 12, 2013
4) Find the missing terms in the arithmetic sequence: 2, ___, ___, ___, 0
a2 = 3/2, a3 = 1, a4 = 1/2
III. Finding the nth Term Given Two Terms
Linear: We know two points: (8, 85) and (14, 157).Find the equation, then find the 5th term.
5) Find the 5th term of the arithmetic sequence with a8 = 85 and a14 = 157.
Book Method:Step 1: Find the common difference
Step 2: Find a185 = a1 + (8 1)(12)
Step 3: Write a rule for the sequence, and evaluate to find a5.an = 1 + (n – 1)(12)
a5 = 1 + (5 – 1)(12) a5 = 49
Alg2 Notes 9.3.notebook April 12, 2013
6) Find the 11th term of the arithmetic sequence with a2 = 133 and a3 = 121.
The 11th term is –25.
IV. The Sum of the First n Terms
Book Method:
= –1449
7) Find the indicated sum for the arithmetic series.S18 for 13 + 2 + (–9) + (–20) + ...
Linear: We know two points: (1, 13) and (2, 2).Find the equation, then find the 18th term. Then use the formula.
Alg2 Notes 9.3.notebook April 12, 2013
8) Find the indicated sum for the arithmetic series.
315
V. Application
9) The center section of a concert hall has 15 seats in the first row and 2 additional seats in each subsequent row. How many seats are in the 20th row?
How many seats in total are in the first 20 rows?
Alg2 Notes 9.3.notebook April 12, 2013
VI. Your Calculator
This formula is for partial sums. Can you find the complete sum of an infinite arithmetic series?
Alg2 Notes 9.3.notebook April 12, 2013
9.3 p.648 #3 45 (x3), 54, 56, 60
Some Extra, do now: 1. a. Find the sum of the first 30 terms of the series 20 + 18 + 16 + 14 + ...b. Find n such that Sn = 760.