Pooh and Alli say:
- Tuesday started out with a POD, as usual.
The POD was:
t3= -7
t6= -2401
Find t10.
- After a few minutes of work, Jaime went up to the board.
His solution:
1. Find out how many jumps
T6 - T3 = 3 jumps *From t3 to t6 there are 3 jumps
2.Solve for r,
Set r to the third power because there are three jumps
Then solve by multiplying the third term with r cubed which equals the sixth term.
-7 x r3 = -2401
-7 -7
r3 = 343
r = 7
3. Find out how many jumps are between t3 and t1.
T3 - T1 = 2 jumps
4. The third term divided by r equals t2.
-7/7 = -1 = t2
With t2 you divide it by r which is 7 and equals t1.
-1/7 = t1
5. Apply Geometric Sequence Formula
Tn= t1 x r^(n-1)
T10 = -1/7 x 7^9 Plug in 10 in tn because we are looking for the tenth term
T10 = -5,764,801
OR
- As Rumidog said, another way of solving the problem, is by assuming that T3 is T1, so that T10 becomes T8.
T8 = -5,764,801
After a while of struggling with the POD and getting some sense out of Jaime’s work most of the class understood the process. You do not need to know the formula to solve the problem, you need to understand how a sequence works.
- Definitions:
Finite Sequence: problems we have already solved.
Infinite Sequence: a sequence that goes on forever.
May or may not have finite limits.
- Limits
Limit: Think of it as a boundary. May or may not reach it, but can never exceed it.
- Bouncing Ball Sequence:
The bouncing ball sequence had a limit:
100, 50, 25, 12.5…
¨The limit of tn as n approaches infinity is zero¨
Lim (tn) = 0
n-->∞
Lim (tn)= ? What happens to n as it gets really big?
n-->∞
The sequence, Tn=n
Write out the first terms of the sequence? Write the limit if possible.
Sarah says the first four terms of her sequence
1, 2, 3, 4
****For a LIMIT to exist it must be a REAL #!!!***
The sequence, Tn=n
The limit Does Not Exist DNE
- To explain why a Limit does not exist, write the following:
Lim(tn) = ∞
n-->∞
- New Sequence
-1, -4, -9, -16,…
What is the Limit?
Lim(tn)= - ∞ DNE
n--> ∞
Lim (tn) = 0
n-->∞
New Problem:
Solve. Find Limit.
The grains of salt on an infinite chess board?
1,2,4,8
Answer- DNE
Lim(tn)= 8
n->8
- New Sequence-
½, ¾, 7/8, 15/16…
Write Limit.
How to solve:
One way is to put them in decimals.
In this sequence, numerator can not be greater than the denominator.
NOTE:
Test is next week: it will have- sequences, series and limits
Remedial Tomorrow
NEXT SCRIBE IS JAIME!!
1 comment:
Sir, I am sorry that some of the formulas are not written nicely. We had problems with the symbols, both pasting them and trying to do ones.
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