ACKNOWLEDGEMENT

We would like take this wonderful opportunity to wish a lot of thanks from our bottom of heart. We have learnt many things directly and indirectly throughout this mathematics coursework. All the more, we gained many extra knowledge and it was a great fun of doing such a coursework as it involves something regarding our daily life. We practised to be punctual when a meeting was put up to carry out the assignment. On the other hand, we build up our understanding towards each other and strengthen our cooperation. It was also enhancing our knowledge on the topics involved in the assignment.

First and foremost, we would like to wish our greatest thanks to God since he gave us the patience and calmness in doing the assignment well. As there is no building without basement, we had our lecturer, Puan Azyanzuhaila who had been guiding us to do the assignment as perfect as possible. She had given us some tips on how to make the assignment to be presentable and the details on how to carry on smoothly with the assignment.

Last but not least, we would like to show our gratitude to our parents who support us economically. We would like to thank our friends who really shares information with us without showing any depression.

We had put our full effort to complete the assignment as we wished. May the work gives the best satisfaction.

“Best cooperation is the key to success”

Thank You.

ARITHMETIC SEQUENCE

1. Mr.Khalid buys a Home Teather System for his new house. Every month he pays his monthly payment. Determine how long it will take to repay a debt of RM7975 by monthly payments of RM10 initially increasing by RM5 each month. How much is the final payment?

Solution:

The monthly payments in RM are10, 15, 20,..........................

which is an arithmetic progression.

The formula for the sum of an A.P. involving the first n terms is:

Sn = n [2a + (n – 1)d] 2

The first payment is RM10, a = 10. The increment is RM5, d = 5. The sum of the payments is the debt of RM7975, Sn = 7975.Substituting into the formula,

7975 = n [2(10) + (n – 1)(5)]2

15950 = n(5n + 15)

n2 + 3n – 3190 = 0

(n – 55)(n + 58) = 0

n = 55 [n = -58 is rejected]

Therefore, the time taken to repay the debt is 55 months.

The final payment or the 55th payment

U55 = a + (n – 1)d

= 10 + (55 – 1)(5) = 280

Therefore, the final payment is RM280.

Solution by graphic calculator for A.P To use the TI-84 PLUS for the Arithmetic sequences and series, we need to change the mode to sequential (Seq)

Press MODE , select Seq

Press Y= and we can notice that this display is different than the display for Y= from the mode FUN

From this display we find

a) Nmin = the smallest termb) u(n) = formula for nth term

= (n-1)th term + difference= u(n-1) + difference

c) un(min) = the first term

Now, key in the formula for Tn

Key in u(n) = as 2nd [u] ( X, T, θ, n - 1 ) + 5

Key in u(nMin) = 10

To find the sum of S26 from the arithmetic series above, we can create a summation formula in v(n)

Sum of the nth term = sum to the term (n-1) + nth term

v(n) = v(n – 1) + u(n – 1) + 5

and v(nMin) = 10

Key in the settings in TI-84 PLUS

Press 2nd [table] and move the cursor to find the value S55

From this table we can find the time taken to repay the debt is 55 months when the S55 shows v(n)=7975

We also can find the final payment of T55 RM 280.00 u(n)

GEOMETRIC SEQUENCES

2. Mr. Razak has planned to invest in an insurance company. If RM100 is invested each year at 5% interest compounded annually, what would be the total amount of the investment Mr. Razak has made after 10 years (before the 11th deposit is made)?

After 1 year the amount invested will have added to it the interest for the year. Therefore, for the last (10th) RM100 invested, its value will become

RM100(1 + 0.05) = RM100(0.05) = RM105

The next to last RM100 will have interest added twice. After 1 year its value becomes RM100(1.05), and after 2 years it is RM100(1.05)(1.05) = RM100(1.05)2. In the same way, the value of the first RM100 becomes RM100(1.05)10, since it will have interest added 10 times. This means that we are to find the sum of the sequences

100(1.05) + 100(1.05)2 + 100(0.05)3 +......+ 100(0.05)10

1 year in 2 years in 3 years in 10 years in account account account account

or

100[1.05 + (1.05)2 + (1.05)3 +......+ (1.05)10]

For the sequences in the brackets, we have a1 = 1.05, r = 1.05, and n = 10. Thus,

S10 = 1.05[1 – (1.05) 10 ] = 13.2068 1 – 1.05

The total value of the RM100 investments is 100(13.2068) = RM1320.68. We see that RM320.68 in interest has been earned.

Solution by graphic calculator for G.P To use the TI-84 PLUS for the Geometric sequences and series, we need to change the mode to sequential (Seq)

Press MODE , select Seq

Press Y= and we can notice that this display is different than the display for Y= from the mode FUN

From this display we find

a) Nmin = the smallest termb) u(n) = formula for nth term

= (n-1)th term x ratio= u(n-1) x ratio

c) un(min) = the first term

Now, key in the formula for Tn

Key in u(n) = as2nd [u] ( X, T, θ, n - 1 ) x 1.05

Key in u(nMin) =1.05

To find the sum of S26 from the arithmetic series above, we can create a summation formula in v(n)

Sum of the nth term = sum to the term (n-1) + nth term

v(n) = v(n – 1) + u(n – 1) x 1.05

and v(nMin) = 1.05

Key in the settings in TI-84 PLUS

Press 2nd [table] and move the cursor to find the value S55

From this table we can find the S10 shows v(n)=13.2068

The total value of the RM100 investments is 100(13.2068) = RM1320.68. We see that RM320.68 in interest has been earned for the 10th years.

REFLECTION BY YOGANANTHARAJ:

I’m Yoganantharaj S/O Renganathan, would like to take this great opportunity to

share my experience doing this mathematics assignment. I have good and bad times

while finishing this task. I would like to thank the God because gave me such a

wonderful chance to improve my knowledge on mathematic skills.

Good guidance of our lecture, Pn.Azyanzuhaila an essential one for our task.

She will always listen to our problems patiently and gave us the explanation with her

own way. She really makes us work with this task smoothly without much pressure. I

really appreciate her with my whole heart with as she shares her previous time in

clearing my doubts upon completing this task. Her encouragements produce self-

confidence in me to proceed with the task. I can still recall the hasting moments

where I really struggled a lot in understanding some concepts of discipline

management.

We are divided into several groups to present our tasks. I worked together with

my group members; Sivanathan and Ravind to produce an effective work. We are

three given a topic two weeks before to prepare our task. I did not felt hard to work

with my group members because I have been worked with them before this. My last

experience with them helps me to move smoothly among the group members to

finish up my task.

We took two weeks to complete this assignment. We faced many problems when we

conduct this assignment. Such as finding notes, friends cooperation, time

management and the list goes on. Our lecturer’s guideline were very helpful to

complete this assignment in time. From this assignment we got a lot of knowledge

about the AP and GP. Apart from that, I also learn the mathematics skills and

techniques of problem solving.

Lastly, I would like to thank to my Mathematics 1 lecturer Pn.Azyanzuhaila Bt

Hasan Basri and also my thanks to my friends.

Reflection

Im Sivanathan s/o Anbu selvam would like to thank the God because gave me such

a chance to improve my knowledge on students discipline management. In group of

three we discussed about the assignment which is about problem solving. Lecturer

also helped us and gives full support to our group to do this assignment.

Furthermore, he also gave some idea and corrects our mistakes that made in our

assignment

Firstly, I try to understand more about the question. Then, I planed work to get the

information various source I searched it from internet and mathematic reference

books in library. After that we collect all the information we got from many resources.

Me with my friends Yoga and Ravind work as a group to finish this assignment. By

finishing this assignment, we also had chance to know about us. This assignment

helped us to build our team work. They finished this assignment successfully.

By doing this assignment I have chance to discover about the arithmetic and

geometric progression and also know about the usage of this progressions in our

daily life.

By using this golden opportunity to thank and apologize to everybody especially my

lecturer, and my classmates if any mistaken that I have made.

REFLECTION

My Mathematics’ lecturer Pn. Azyanzuhaila gave us a group assignment which is about

arithmetic and geometric progression. In group of three we discussed about the assignment. My

lecturer also helped us and give us full support to do this assignment. He also gave some idea and

corrected our mistakes besides motivate us by his words.

After we discussed in group, we started to search information from many sources. For

example, we searched in newspaper, internet, and magazines. We also searched in many revision

books about a.p. and g.p. which required in this assignment. We search thoroughly and specifically

about a.p. and g.p.

By doing this assignment, I can clearly understand the meaning of a.p. and g.p. I was also

able to clarify my confusions on the types of a.p. and g.p. in a mathematics question. In addition, I

also identified many methods to solve a.p. and g.p. questions.

When we did this assignment in groups, we were able to understand each other very well

and were able to divide our woks in balance. We co-operated very well and everyone was very

helpful to one another when we did our Mathematics assignment in groups.

Last but not least, we thank to everybody who kind heartedly lend their hand to do this

assignment completely and successfully. I like to use this golden opportunity to thank and everybody

especially my lecturer, and my classmates for their support and help.

Prepared by,

…………………………………

(RAVIND A/L SIVALINGAM)