Download 9.2 Arithmetic Sequences.notebook

9.2 Arithmetic Sequences.notebook
Bellwork
January 26, 2016
9.2 Arithmetic Sequences
Find the first, second, third, and tenth term for
explicit formula.
Objectives:
• Find the nth term of an arithmetic sequence.
• Find the sum of an arithmetic series.
an = -5n + 1
Jan 8­7:08 AM
Jan 8­7:08 AM
Arithmetic Sequence:
A sequence in which each term after the first term is found by adding or subtracting the previous term by a constant d, called the common difference.
Example 1: Given the following sequences of
numbers, decide whether it is arithmetic. If so,
state the common difference.
a. 3, 6, 9, 12, 15, ...
Common Difference:
b. 12, 14, 18, 22, ...
c. 6, 12, 18, 24, 30, ...
a1 – the first term in the sequence.
Jan 8­7:10 AM
Jan 8­7:12 AM
Example 2a: Finding the common difference and
the next three terms in the
arithmetic sequence
Example 2b: Finding the common difference and
the next three terms in the
arithmetic sequence
1, 5, 9, 13,...
10, 20, 30, 40,……..
d=_______, a5 = ____, a6 = _____, a7 = _____
Jan 8­7:13 AM
d=_______, a5 = ____, a6 = _____, a7 = _____
Jan 8­7:13 AM
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9.2 Arithmetic Sequences.notebook
January 26, 2016
Writing an Explicit Formula for Arithmetic Sequences:
Writing a Recursive Formula for a Arithmetic Sequence:
1. Determine that the sequence is arithmetic.
2. Identify the common difference. 3. Create an explicit formula using the first term in the sequence and the common difference.
1. Determine that the sequence is arithmetic. 2. Identify the common difference.
3. Create a recursive formula using the first term in the sequence and the common difference.
Arithmetic Formula
an= a1 +d(n – 1)
a1 = first number
an = ( an­1 ) + d
Jan 8­8:46 AM
Jan 10­7:32 AM
Example 4: Suppose you are saving for a brand new Iphone, you start with $50 and save $10 each week.
a) Write a sequence of numbers that represents how much you have saved at the end of each week.
b) What is the common difference?
c) Write an explicit formula to represent the situation.
Jan 12­10:22 AM
Example 4: Suppose you are saving for a brand new Iphone, you start with $50 and save $10 each week.
d) Write a recursive formula to represent the situation.
Jan 12­10:39 AM
Assignment
9.2 Worksheet
e) Use the explicit formula to find how much you saved at the end of the 10th week. Jan 12­10:39 AM
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