Lesson 5: Discover | MoodleHUB 🎓

1. Lesson 5

1.4. Discover

Mathematics 20-1 Module 1

Module 1: Sequences and Series

Discover

This is an image of a castle on a chessboard.

Try This 1

Legend has it that the game of chess was invented for a Persian king by one of his servants. The king asked the servant how he would like to be paid for the game. The servant stated that he would like one grain of rice to be placed on the first square of the chessboard, two grains of rice to be placed on the second square, four grains of rice on the third square, eight grains of rice on the fourth square, and so on. Each subsequent square was to have twice as many grains of rice than the previous square.

Complete the chart.

Square	1	2	3	4	5	6	7	8	9	10
Number of Grains of Rice in the Square	1	2	4

Write an expression that represents the numbers of grains of rice, R, on the nth square of the chessboard.
Determine the total number of grains of rice in the first
1. 5 squares
2. 9 squares
Analyze your answers to question 3. Describe a strategy that could be used to determine the total number of grains of rice in the first n squares.

Save your results in your course folder.

Share 1

Share your strategies with a partner. Find out the total number of grains of rice up to and including 15 squares or more. Compare your strategies with your partner's strategies to see if both strategies yield identical results.
Describe how the strategy could be adapted to solve the following similar problem:

A second servant solved another problem for the king. Granted the same wish as his companion, the second servant asked for 2 grains of rice on the 1st black square, 8 grains of rice on the 2nd black square, 32 grains on the 3rd black square, and so on. Each subsequent black square was to have four times as many grains of rice than the previous black square.

Save your results in your course folder. You will use these results later in the lesson.