Chapter 4.1, Problem 65E

When we square a whole number of fraction, the number we obtain is called a prefect square. For example, 9 is a perfect square since when we square the number 3 we obtain 9. In exercises 65 and 66 we will look at a relationship that exists between the sequence of perfect square and the sequence of positive odd number. This relationship was investigated in the thirteenth century by an Italian mathematician names Leonardo of Pisa, also known as Fibonacci.

a. List the first 6 odd numbers.

b. Complete the green table as follows. In the third row, write the first 3 odd numbers, in

the four row, white the 4 odd numbers, and so on.

c. In the blue boxes, white the sum of tee odd numbers.

d. In the orange boxes, white each sum in exponent form.

e. Describe the pattern observed with the set of numbers in the blue boxes.

f. Describe the pattern observed with the set of numbers in the orange boxes.

g. Based in the observations made in exercises 65(e) and 65(f), fill in the last four black boxes.

h. Observe the pattern above and complete the following.

The sum of the first 12 positive odd numbers equals: ${\boxed{}}_2$

The sum of the first 20 positive odd numbers equals: ${\boxed{}}_2$