SEQUENCES

MATHS SEQUENCES

Exercise 1

Using Excel load the spreadsheet called SEQUENCE. The spreadsheet is stored on drive s.

2.1O	Number software	3
2.2A	Find information by looking in the right directory	3
2.2B	Find information by looking for files with a given name	3

The grid below appears on your screen.

PUT YOUR NAME IN THE SPACE PROVIDED

Look at the "SEQUENCES" worksheet you did last lesson. You should have found that the formula for sequence A was n + 1. You are going to enter this formula on the spreadsheet into cell f4.

HOWEVER, The computer will not understand the formula in terms of n.

2.1A	Select appropriate information taken from existing sources	3
2.2F	Number information	3
2.2I	Software for numbers	3

The formula tells us that to work out each term of the sequence we need to add one to the term number. The first term number is stored in cell d4. So into cell f4 enter the formula =d4 + 1. "2" should appear in cell f4.

2.2J	Edit information: Amending	3
2.2K	Edit information: Moving	(3 )
2.2L	Edit information: Reformatting	(3 )
2.2N	Edit information: Deleting	(3 )
2.2O	Edit information: Inserting	3

This formula now needs to be copied down the whole column to see if it works for each term. Use the FILL DOWN command to do this. Check that the numbers on your spreadsheet match the answers you obtained on the worksheet.

2.2M

Edit information: Copying

b) Now look at sequence B. You are going to enter your formula for this sequence into cell h4. Remember this must be done in terms of cell d4 and NOT in terms of n. Enter your formula into the spreadsheet.

Does "2" appear in cell h4? FILL DOWN this formula down the whole column. Do all the numbers on your spreadsheet match the answers you obtained on the worksheet?

c) Now try to enter your formulas for sequences C, D, E, F, G and H. Each time FILL DOWN the formula and check that the numbers match.

	Examples of combined text and numerical information. Range below to be ticked as appropriate:
2.3G	Fitness for purpose	3
2.3H	Matched to the audience	3
2.3I	Clarity	3
2.3J	Accuracy	3
2.3K	Appropriate use of information reference	3
2.3L	Consistent format	3

d) When you have finished sequence H obtain a printout.

2.3T

Print-out of presented combined information completed

Exercise 2

The grid below appears on your spreadsheet.

Term	Sequence 1	Guess	Sequence 2	Guess	Sequence 3	Guess	Sequence 4	Guess
1	6		7		4		1
2	12		13		9		5
3	18		19		14		9
4	24		25		19		13
5	30		31		24		17
6	36		37		29		21
7	42		43		34		25
8	48		49		39		29
9	54		55		44		33
10	60		61		49		37

a) Look at sequence 1. What is formula for this sequence?

To check this you will need to enter the formula for this sequence into cell f7. HOWEVER, remember that the computer will not understand the formula in terms of n. When you have entered your formula copy it down the whole column to see if it works for each term. Use the FILL DOWN command to do this.

Now find formulas for the other sequences on sheet 2. Altogether, there are 4 for you to try.

When you have finished all 4 successfully obtain a printout.

SAVE your work with a suitable File Name.

2.1P	Name files sensibly to indicate contents	3
2.1T	Save work when all the information has been input	3
2.2R	Save information before and after important changes	3

b) Now go to sheet 3.

Find formulas for all 4 sequences on sheet 3.

When you have finished all 4 successfully obtain a printout.

SAVE your work in your Network Area

2.1T	Save work when all the information has been input	3
2.2R	Save information before and after important changes	3

c) Now go to sheet 4.

Find formulas for all 4 sequences on sheet 4.

When you have finished all 4 successfully obtain a printout.

SAVE your work in your Network Area

2.1T	Save work when all the information has been input	3
2.2R	Save information before and after important changes	3

d) Now go to sheet 5.

Find formulas for all 4 sequences on sheet 5.

When you have finished all 4 successfully obtain a printout.

SAVE your work in your Network Area

2.1T	Save work when all the information has been input	3
2.2R	Save information before and after important changes	3

Now, make Backup copies of your work onto your floppy disk.

2.1U	Examples of back-up copies of files	3
2.2S	Save information when the processing is complete	3
2.3U	Back-up copies of files containing combined information made	3

Now go to sheet 6.

Exercise 3

The grid below appears on your spreadsheet.

Term	Fibonacci Number	Task 1	Task 2	SUMS
f1	1
f2	1	A
f3		B	x
f4		C	y
f5				s
f6				t

It shows the first 2 terms of a FIBONACCI SEQUENCE. Use a formula to complete the first 20 Fibonacci numbers. Note that we call the first Fibonacci number f1 the second f2 the third f3 etc. You should find that f20 is 6765.

TASK 1

In the column headed TASK 1 go to the position marked a. Into this cell put a formula to find the result of f12 + f22 . In position b put the result of f22 + f32. In position c put the result of f32 + f42 and so on down the whole column.

TASK 2

In the column headed TASK 2 go to the position marked x. Into this cell put a formula to find the result of f22 – f1f3. In position y put the result of f32 - f2f4 and so on down the whole column.

What is the value of fl002 – f99f101 ?

SUMS

In the column headed SUMS go to the position marked s. Into this cell enter a formula which will add up the first 5 Fibonacci numbers. Into position t enter a formula which will add up the first 6 Fibonacci numbers and so on down the whole column. What can you predict about the sum of the first 20 Fibonacci numbers?

EXTENSION TASKS

Go to sheet 7

Exercise 4

a) Create your own spreadsheet as below.

Term	Fibonacci Number	DIVIDE
F1	1
F2	3	A
F3		B
To
F30

b) Complete the "Fibonacci Number" column to obtain the first 30 terms of this Fibonacci sequence. You may need to widen the DIVIDE column.

c) Now complete the "DIVIDE" column as follows:

In the cell marked a enter a formula to find the value of f2 divided by f1. In the cell marked b enter a formula to find the value of f3 divided by f2 etc.

Look closely at the numbers. What do you notice?

d) Now try with a different Fibonacci sequence. Choose your own values of f1 and f2. The formulas will automatically recalculate the Fibonacci numbers and the divisions.

Look closely at the numbers. What do you notice?

e) Repeat for other Fibonacci sequences of your own choice.

f) In a blank cell calculate the value of (1 + Ö 5)/2. This is a special number. Can you find out what it is called?

FINAL TASK – Produce a printout of your directory to show that you saved your files in a sensible location

2.1Q

Locate files conveniently for future use (File directory printout)

EVALUATION ACTIVITY

Write a short evaluation of this activity. The evaluation should include:

Explain why you used Excel for the activity

What were the advantages of using Excel over using a piece of paper and a calculator?

Were there any disadvantages with using Excel?

What features of Excel did you use and how did they help you?

2.4A	Explain the reasons why you have chosen to use information technology for a particular task	3
2.4C	Compare manual methods of completing tasks with those involving the use of information technology	3
2.4D	Describe the features of software facilities which you have used in completing a task	3

ASSESSOR OBSERVATION

2.1I	Correct errors noticed on entry (Assessor Observation)	(3 )
2.1J	Put right simple equipment faults (Assessor Observation)	(3 )
2.1K	Use manual and on-line help facilities	(3 )
2.1L	Ask for help as appropriate	(3 )
2.1S	Save work before and after important changes (Assessor Observation)	3
2.3S	Records of observation by the assessor of information displayed on screen obtained (Assessor Observation)	3

EQUIPMENT FAULTS AND ERRORS LOG

2.4E

Describe the errors and equipment faults that occurred during the completion of a task involving inf. Technology and the effects of this

(3 )