Regularidades 1

	HERE'S AN APPETIZER
	3rd year of secondary education

1. VERY EASY

In this window you can see the 6 first terms of five series of numbers. If you change the value of the parameter a different series will appear, which follows the same pattern as the original one.

1.- What's the next number in each of the five original series?

2.- Change the parameters to those which appear in the table below and complete the table with the missing information.

Parameter	Next term
n	series 1	series 2	series 3	series 4	series 5
8
15
23
30
40

3.- Form five different series, which follow a similar pattern to the ones on the electronic board, so that the sixth term in each case is 8.

2. FINDING OUR WAY
In this window there are four series and there are four numbers in each series. The two middle numbers have been replaced by zero and we don't remember what these numbers were. We only know that in order to achieve our aim of finding the last number in each series we should add, subtract, multiply or divide each term by the same value, which we have also forgotten. Furthermore, the electronic board isn't working very well, so we can only change the parameter values by using the mouse and keyboard.
	4.- Try different parameter values until you find the "key" number in each sequence. You will know when you've got the right answer as 1 will appear in the correct answer column instead of 0. 5.- When you have found the four key numbers explain how each series is formed in your exercise book. 6.- Form six more series which are similar to the ones above and give them to your classmates to try and work out.

3. FINDING THE RULE

There are five number sequences in this window. As you change the parameter you will see how we move along the sequence term by term. The number n tells us the position in the series of the first term that appears on the screen.

7.- Write the first fifteen terms in each series in your exercise book.

8.- Use the electronic board to find out where the following terms appear in each series: 25, 38, 50, 80.

9.- Would you be able to write down the rule which explains how each series is formed? (You're not going to write a formula)

10.- Can you work out the equations we need to find any term in each series given their position in the series? (Be very careful with this question!)

	Josep Mª Navarro Canut

	ProyectoDescartes.org. Year 2013