eQuizShow

Sequences and Series

Arithmetic Sequence

Question: An arithmetic Sequence is a pattern of numbers whose terms have a common _______________.
Answer: difference

Question: The arithmetic sequence follows the pattern 3n-7.  What would be the 15th term in the sequence.
Answer: 38

Question: Find the explicit nth term equation given the sequence:
21,28,35,42, .....

Answer: a(n) = 7n +14

Question: Find the arithmetic sequence given that the 3rd term is 40 and the 5th term is 20.
Answer: a(n) = -10n + 70

Question: An arithmetic sequence can be said to be closely related to what type of algebraic function?
Answer: Linear

Geometric Sequence

Question: A Geometric Sequence is a pattern of numbers whose terms have a common _______________.
Answer: ratio

Question: The geometric sequence follows the pattern 0.5(3)^n-1.  What would be the 5th term in the sequence.
Answer: 40.5

Question: Find the explicit nth term equation given the sequence:
7,21,63,189, .....

Answer: a(n) = 7(3)^n-1

Question: Find the geometric sequence given that the 3rd term is 10 and the 5th term is 40.
Answer: a(n) = 2.5(2)^n -1   AND a(n)=2.5(-2)^n-1

Question: A geometric sequence has been said to be closely related to what algebraic function?
Answer: Exponential

Arithmetic Series

Question: Define an arithmetic series.
Answer: the sum of a pattern of numbers that have a common difference.

Question: Find the sum of the first 10 terms of the sequence 2n + 1.
Answer: 120

Question: Find the sum of terms 5 through 10 of the sequence 2n + 1.
Answer: 96

Question: The arithmetic sequence is:
2,4,6,8,10......  What would be the sum from 1 to infinity?

Answer: Infinity

Question: What is the sum of the sequence (1/3)n - 182 for the first 352 terms.
Answer: -43,354.67

Geometric Series

Question: Define a geometric series.
Answer: The sum of a pattern of numbers with a common ratio.

Question: Find the sum of the first 10 terms of the sequence 3(2)^n-1
Answer: 3069

Question: Find the sum of terms 5 through 10 of the sequence 3(2)^n-1
Answer: 3024

Question: The geometric sequence is:
3,9,27,81.......  What would the sum from one to infinity be?

Answer: divergent, to infinity

Question: The geometric sequence is:
81,27,9,3.......  What would the sum from one to infinity be?

Answer: 121.5

Mix

Question:

Explain the difference between a diverging infinite geometric series and a convergent geometric series.  Please include the “r” value in your discussion along with other valid points.



Answer: abs(r) < 1 then converges and abs(r) > 1 then diverges to infinity

Question: Why do we sometimes end up with two "r-values" and answers with a geometric sequence? List two reasons.
Answer: 1.) don't know enough info, the pattern may go +/- or +/+ or -/-.
2.) The r-value will have an even power resulting in a +/- in front of the problem.


Question: What does it mean to be a modeling problem?
Answer: -uses real life problems within, aka word problems

Question: Please tell the formula one would use to find the sum of a converging infinite geometric series.
Answer: (a1) / (1- r)

Question: What is the difference between a partial sum and an infinite sum?
Answer: infinite adds all numbers forever and partial has set limits.