Solve It! A wooden post-and-rail fence with two rails is made as shown.
Find the number of pieces of wood needed to build a 4-section fence, a 5-section fence, and a 6-section fence. Not all items will be used.
26 pieces
25 pieces
13 pieces
16 pieces
20 pieces
27 pieces
24 pieces
19 pieces
4-section fence
5-section fence
6-section fence
Take Note: Define sequence.
Take Note: Define term of a sequence.
Problem 1 Got It?
Problem 1 Got It?
Problem 1 Got It?
Problem 1 Got It?
Take Note: Define arithmetic sequence.
Take Note: Define common difference (of an arithmetic sequence).
Take Note: Provide an example of an arithmetic sequence with a common difference of 3 that includes 5 terms.
Problem 2 Got It?
Problem 2 Got It?
Problem 2 Got It?
Problem 2 Got It?
TAKE NOTE Key Concept
Recursive Formula For an Arithmetic Sequence
The nth term of an arithmetic sequence with first term A(1) and common difference d is given by
Take Note: Define recursive formula.
Problem 3 Got It? Write a recursive formula for the arithmetic sequence.
Problem 3 Got It? What is the 9th term of the arithmetic sequence?
Problem 3 Got It? Write a recursive formula for the arithmetic sequence.
Problem 3 Got It? What is the 9th term of the arithmetic sequence?
Problem 3 Got It? Write a recursive formula for the arithmetic sequence.
Problem 3 Got It? What is the 9th term of the arithmetic sequence?
Problem 3 Got It? Write a recursive formula for the arithmetic sequence.
Problem 3 Got It? What is the 9th term of the arithmetic sequence?
Problem 3 Got It? Reasoning: Is a recursive formula an efficient way to find a value of a term in an arithmetic sequence?
HINT: What if you want to find the 91st term in an arithmetic sequence and only have the first term and recursive formula? You would have to know the 90th term. To know that, you would have to know the 89th term...etc.
Take Note: Define explicit formula.
Problem 4 Got It?
Problem 4 Got It?
Problem 5 Got It?
Problem 5 Got It?
Problem 6 Got It?
Problem 6 Got It?
Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?
Take Note: In a recursive formula, why is it important to define the first term of the sequence?
Take Note: In a recursive formula, what does n represent?
Take Note: In a recursive formula, what does A(n) represent?
Take Note: In a recursive formula, what does A(1) represent?
Take Note: In a recursive formula, what does d represent?
Take Note: In an explicit formula, what does n represent?
Take Note: In an explicit formula, what does A(n) represent?
Take Note: In an explicit formula, what does A(1) represent?
Take Note: In an explicit formula, what does d represent?
