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, \dots

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.

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320

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