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Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 54 Page 320

Practice makes perfect

a

We want to write a sequence formed by the side length of the square shown in the diagram.

Let's make a table to organize the terms.

Square n	1	2	3	4	5	6
Length, a_n	1	1	2	3	5	8

We get the sequence below. 1, 1, 2, 3, 5, 8, ...

b

The name of the sequence is the Fibonacci Sequence, in which each term is the sum of the two previous terms except for the first two terms.

a_1=1, a_2=1, a_n=a_(n-2)+a_(n-1) To find the next term, we need to find the sum of a_5 and a_6. a_5+a_6=a_7 ⇕ 5+8 = 13 The seventh term is 13.

c

Since the next term is 13, we need to add a square with side length 13 to the diagram. We will place this square underneath the diagram since the spiral grows downwards.