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Tuesday, January 17, 2006

Geometric Sequence!

Hello, I am so not Sith Lord Darth SAMUS! That would mean that I'm like Darth Vader's sister or whatever. I don't want to be his sister, maybe his wife. Yes, well you all know that I'm the scribe for today. Anyways, Mr. Kuropatwa put up 3 different sequences on the board and we had to find the next 3 that come after each sequence. Here were the three sequences he put up,

sequence: 3, 6, 12...
Next 3: 24, 48, 96
Rule: 3. 2^19

Sequence: 81, 27, 9...
Next 3: 3, 1, 1/3
Rule: 81. 1/3^19

Sequence: 4, -8, 16...
Next 3: -32, 64, -128
Rule: 4. -2^19

The first sequence we have 3, 6, and 12. The next three is 24, 48, and 96. You must be wondering how we got the answer. I know most of us just multiplied the number before the term we're figuring out by 2. That's right, but it's more difficult than that. There's a formula that would make your life easier when solving similar problems. To find the nth term in a geometric sequence is tn= t1(r)^(n-1)
And for the second sequence you notice that whatever the number is you divide by 3. So the common ratio is 1/3. In the third sequence the common ratio is multiply by -2.
We also put in new stuff in our math dictionaries. I can't believe that it's the last entry! This semester went by quite fast. What we put in our dictionaries were,

Geometric Sequences:
i) Recursive definition: an ordered list of numbers generated by continuously multiplying a given first term by a given value (common ratio).
ii) Implicit definition: an ordered list of numbers where each number in the list is generated by an exponential equation.

Common Ratio:
I) The number that is repeatedly multiplied to successive terms in the sequence.
ii) From the implicit definition r is the base of the exponential function.

To find the nth term of a geometric sequence:
tn= t1r^(n-1)

tn is the nth term
n is the rank of the nth term
t1 is the first term
r is the common ratio

And that's the end of our math dictionary... For now. Later on in life we'll have to make dictionaries for different subjects and maybe once again in grade 11. It's kind of sad when you think of it, well I'm kind of bummed. I like our math class. Yes, well after our dictionaries most of us worked on our Go for Gold! If you weren't working on Go for Gold we were assigned to do exercise 62, the whole thing. I guess this is my last time being scribe. For tomorrow, our scribe is...... madam Melissa V! Haha, see you all tomorrow!


At 1/17/2006 9:35 PM, Blogger Mr. Kuropatwa said...

SAMUS, this is an OUTSTANDING scribe post. Something I can show students in my next class what a scribe post should look like. Bravo!

BTW, arithmetic sequences have common differences, geometric sequences have common ratios. You can always go back and edit your post. That would make it just about perfect. ;-)


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