the SCRIBE POST for Jan.13,2006

Hello, I'm Sir Tim-Math-y, your scribe for today and by the way, you can call me Tim or Timmy for short.

Previous to today's class, maybe 15 minutes before class, Diyaa won in chess vs Mr. Kuropatwa? Goodjob.

During todays class, we started off by going over two questions from last night's homework - exercise #60. We looked over questions 1.a) and 2.

1. a.) Find the sum of the arithmetic sequence: 2,5,8,11, ... to 25 terms.

We used the following equation:
Sn = n/2[2t1+(n-1)d]
S25 = 25/2[2(2)+(24-1)3]
S25 = 25/2[76]
S25 = 950

2. Find the sum: 4+7+10+ ... +73

By utilizing the recursive equation "tn = t1+(n-1)d" we found that we could replace 73 with tn to find the unknown "n". (There was also another way that Kim mentioned that you could also use but I'll try to keep this as simple as possible)
73 = 4+(n-1)3
73 = 4+3n-3
73 = 3n+1
72 = 3n
24 = n

Now by using the now known value of "n", we used the equation that finds the sum of numbers in a sequence.
Sn = n/2[2t1+(n-1)d]
S24 = 24/2[2(4)+(24-1)3]
S24 = 12[77]
S24 = 924

After we were finished quickly answering some uncertainties, we added more to our Math Dictionaries. If you weren't here to get this, I will put it up on the blog so that you can.. stretches fingers**.

TO FIND THE Nth TERM IN AN ARITHMETIC SEQUENCE
tn = t1+(n-1)d
tn is the nth term
t1 is the 1st term
n is the rank of the nth term in the sequence
d is the common difference

EXAMPLE: Find the 51st term in the sequence: 11,5,-1,-7, ...

t1 = 11
d = 5-11
= -6
n = 51

t51 = 11+(51-1)(-6)
t51 = 11+50(-6)
t51 = 11-300
t51 = -289

ARITHMETIC SERIES
The sum of numbers in an arithmetic series is given by:
Sn = n/2[2t1+(n-1)d]
Sn is the sum of the nth term in the sequence
n is the rank of the nth term
t1 is the 1st term
d is the common difference

EXAMPLE: Find the sum to the 30th term in the sequence:
11,5,-1,-7, ...

t1 = 11
d = 5-11
= -6

S30 = 30/2[2(11)+(30-1)(-6)]
S30 = 15[22+(29)(-6)]
S30 = 15[22-174]
S30 = -2280

This is all that will go into your dictionary for today only. Mr. K said that there will be more that will come in time.

After we were done with our math dictionaries, we did some practice questions. Unfortunately, I only have the answer to the first question so that will be the one on the blog.

1.) Joe bought a painting for $1800. After 7 years, the artist became world famous and the painting sold for $14000. If the value of the painting appreciates arithmetically, determine the amount of appreciation and the value of the painting 28 years after it was 1st purchased.

This is the arithmetic sequence: $1800,$14000,_______,_______,_______
The last blank in the sequence (term5) is what we are trying to find. We do so by using the recursive formula.

tn = t1+(n-1)d
t5 = 1800+(5-1)12200
t5 = 1800+48800
t5 = 50600

In 28 years, the painting will cost $50600 (that's alot of money)

That is basically all we did today.

Advice of the Day:
"To study for the exam, you can rewrite your math dictionary using your senses (read it out loud so that you can hear what you are writing). It has helped many in the past." - Mr. Kuropatwa

Projects and our Last Test:
Mr. K says that we will get our projects back on monday and the test, he says we will get back sometime next week.

Upcoming Unit Test:
Our last unit on Sequences and Series is coming to an end and waiting for us will be the unit test! I believe that Mr. K said that our unit test may be sometime next week so good luck with that.

Homework for the Weekend:
Home work for the weekend is ALL of exercise #61 I think. Also, you should do some of the "Go for Gold" assignment to reduce the work during the following week.. I guess I could've put it under advice too! :D

Scribe:
Grr.. Master Jian, me and Jojo didn't plan on making a website on Bestbuy because making a website for your Restaurant (Hong Hing on Ellice :) ) would be much more cool and it's much easier!
Sooo.... Monday's Scribe will be... Commander "John D. - #12" for no reason at all.. hehe.

Well that's the end of my Scribe post, have a great WEEKEND!!! ... I hope I didn't forget anything..