Scribe Post 05/17/07

POD 5/17/07

The east section of a sports stadium has 30 rows of seats. The tenth row has 100 seats and every row has 3 more seats than the row below it. How many seats are in the east section of the stadium?

Melissa answered:

10th row=100 seats d=3 amount=30 rows t30=?

Find t1
10-1=9 = 9jumps
9 * 3(distance) = 27
100-27=73
t1=73

2. tn=t1+(n-1)d
t30=73+(30-1)3
t30=160

Sn=n/2(t1=tn)
S30=30/2(73+160)
S30=15(233)
S30=3,495 seats

Different way for finding t1

t1= t10 (n-1)-3
t1=100 = (10-1)-3
t1=100-27
t1=73



tn= (.99)^n= whose limit is 0.
(in our graphing calculators)
Graph y=.99^x
Adjust window: Xmin=0, Xmax=500, Ymax=1

*We used this procedure to prove that the limit of the function is 0. This way we acquire a clearer view.

The graph shows that the sequence will never reach or cross the line Y=0.

*The limit is always a Y value(tn for a sequence)
*The limit is a boundary on the range.


Practice: find the Lim tn as n approaches infinity for the following sequences.


*Two acceptable strategies
1. list the 1st few terms
2.THINK


Example 1:
tn=(-n)^2
Answer: the limit of tn as tn approaches infinity = infinity.

First few terms: 1, 4, 9, 16 …. 10,000
The numbers keep getting bigger, therefore there is no limit.

Example 2:
tn=(-1)^n-1(n/10^n)
Answer: The limit of tn as n approaches infinity = 0.

First few terms: 1/10, -1/50, 3/1000, -4/10,000….
While n is approaching infinity, tn approaches 0, however never gets there.


Example 3:
tn=(-1)^n-1*n
n+1
Answer: DNE

First few terms: ½, -2/3, ¾, -4/5…
There is no limit because it isn’t reaching any number, it is isolating between two different numbers.


Sir we had problems with the camera, therefore we werent able to post the graphs. We will post the graphs tomorrow with their explanations, as a comment to the scribe.


Daniel gilchrist and Jorge Vergara