Applications of Sequences and Series

Learning Objective: to apply sequences and series to real world situations

Warm-up (IN)

HW/INB Check!

When you’re finished…grab a quiz!

Notes!

Ex 1 – find the sum of the positive even integers to 100

2 +4+6+…+100

Arith!

1

2n

n

a a nS

2

2 100 502550

Ex 2 – how many multiples of 4 are there between 25 and 75?

28,32, 36, ,…,72

Arith!

We need to find

n

1 ( 1)na a n d 72 28 ( 1)n 4

44 4n 448 4n

12n

Ex 3 – a pump removes 5% of the water in a pool each minute. What % remains after 10 minutes?

11n

na a r

How much is in the pool initially?

100%

1,

How much is in the pool the next minute? 95%

1 .95 ,

Then 95% of that, etc.

21 .95 , 3

1 .95 ,...

How much is in the pool after 10 minutes?

101 .95 .60 60%

1 .05

10a

Ex 4 – John rented an apt in 2003 for $600 a month. If his monthly rent was increased 5% at the end of each year, how much was his monthly rent in 2009?

2003 2004

600, 600 1.05 ,2005

2600 1.05 ,...

11n

na a r

6a 6600 1.05 $804.06

Ex 5 – a stack of cans has 12 cans on the top layer, 13 on the 2nd layer, and so on. If there are 20 cans on the bottom layer, how many total cans are on the display?

12+13+14+…+20 First we need to find n

1 ( 1)na a n d 20 12 ( 1)n 1

8 n 19 n

Now, sum!

1

2n

n

a a nS

2

12 20 9

144

HW – Applications worksheet #1-7

Out – None!

Summary – Sequences and series are useful because…

Don’t forget about POW!!