Complete as many of the following problems as you can by the end of class.

Work in teams if you wish.

1. Write a for loop to sum all the integers between 1 and 100.

2. In 1784, Carl Gauss solved problem #1 in seconds by noticing that:

1 + 99 = 100, 2 + 98 = 100, 3 + 97 = 100 (he was 7 years old at the time.)

Write a for loop to compute the sum in #1 using approximately half the number of executions of the for loop in #1.

3. Write a program that outputs the sequence of numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121

4. Write a program for problem #3 that does not use the multiplication operator (*).

(Hint: look at the difference between each number in the sequence of squares)

5. Write nested for loops to produce this output:

1

2

3

4

5

6. The first 12 Fibonacci numbers are: 1 1 2 3 5 8 13 21 34 55 89 144

Write a program to compute the first 12 Fibonacci numbers.

7. Write nested for loops to produce the following output:

000111222333444555666777888999

000111222333444555666777888999

000111222333444555666777888999

8. Write nested for loops to produce the following output:

1111111111

22222222

333333

4444

55

9. Write nested for loops to produce the following output:

$

$$$

$$$$$

$$$$$$$

$$$$$$$$$