Unit 8 Summary SheetName:

Sequences and Series, Curves of Best Fit and Combinatorics

Sequence Formulas / Series Formulas
  1. Is the sequence arithmetic, geometric, or neither? If the sequence is arithmetic or geometric, identify the common difference or ratio.

Algebra 2 2013-14

  1. –1, 1, 3, 5, …
  1. 3, 8, 9, 12, …
  1. 2, 4, 8, 16, …
  1. –6, –1, 4, 9, …

Algebra 2 2013-14

  1. Find the nth term of the sequence 3, 7, 11, 15, …
  1. Find the nth term of a sequence with d = 2 and a12 = 18.
  1. Find the 100th term of this arithmetic sequence: 5, 8, 11, 14, 17, …

Algebra 2 2013-14

  1. 302
  2. 305
  3. 308
  4. 311

Algebra 2 2013-14

  1. Find the nth term of the sequence 3, 9, 27, 81, …
  1. Find the 10th term of the geometric sequence 1, 4, 16, …

Algebra 2 2013-14

  1. 40
  2. 180,224
  3. 262,144
  4. 2,883,584

Algebra 2 2013-14

  1. Find the sum of the first 20 terms of the series 40 + 37 + 34 + 31 +…
  1. What is the sum of the series ?

Algebra 2 2013-14

  1. 62
  2. 66
  3. 990
  4. 1980

Algebra 2 2013-14

  1. Find the sum of the first 8 terms of the series
  1. What is the sum of the series ?

Algebra 2 2013-14

  1. 216,285
  2. 213,240
  3. 211,909
  4. 25,669

Algebra 2 2013-14

  1. Given a sequence determined by , where is the first term:
  2. What is the 500th term of this sequence? Show your work and explain how you found your answer.
  1. What is an expression in sigma notation for the sum of the first 500 terms of this sequence?
  1. What is the sum of the first 500 terms of this sequence? Show your work, and explain how you found your answer.

12. Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on. If the daily wage keeps doubling, what will your total income be for working 31 days?

  1. You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds?
  1. Ryan is building his Pinewood Derby Race car. To make the car he needs to pick one body style, one color of paint, and one type of wheels. If there are 5 body styles to choose from, 10 colors of paint to choose from, and 3 types of wheels to choose from, how many possible different cars could Ryan come up with?
  1. The football team needs to select 2 of its members to serve as co-captains for the team. If there are 31 members on the team, in how many possible ways can the 2 co-captains be chosen?
  1. A license plate in a certain state must have 3 letters followed by 3 numbers with no repetition allowed. How many possible license plates can be created?
  1. Find the number of distinguishable permutations of the letters in the word: HONOLULU.
  1. A standard deck of 52 playing cards has 4 suits with 13 different cards in each suit.

a)If the order in which the cards are dealt is not important, how many different 5 card hands are possible?

b)In how many 5 card hands are all 5 cards of the same color?

  1. The table shows the numbers of business and non-business users of instant messaging for the years 1999 –2005.

Years since 1998 / 1 / 2 / 3 / 4 / 5 / 6 / 7
Business users (in millions) / 1 / 2 / 5 / 7 / 20 / 40 / 80
Non-business users (in millions) / 55 / 97 / 140 / 160 / 195 / 235 / 260
  1. Determine the mathematical model that best represents the data for business users.
  1. Equation ______r
  1. Approximately how many millions of business users of instant messaging would you expect in the year 2015?
  1. The data below show the average growth rates of 12 Weeping Higan cherry trees planted in Washington, D.C. At the time of planting, the trees were one year old and were all 6 feet in height.

Age of Tree
(in years) / Height
(in feet)
1 / 6
2 / 9.5
3 / 13
4 / 15
5 / 16.5
6 / 17.5
7 / 18.5
8 / 19
9 / 19.5
10 / 19.7
11 / 19.8

a)Determine the mathematical model that best represents the data.

b)Equation ______

c) Approximately how tall is a 19 year-old Weeping Higan cherry tree?

Algebra 2 2013-14