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.