FC: Compare and Contrast
1: Definitions: Computation- is finding an answer by using mathematics or logic. Converges- IrI < 1 Diverges- IrI > 1
2: Series | Series Definition: The sum of the terms of a sequence. The series is infinite (finite) if the corresponding sequence is finite. | Compare: Both the series and the sequence correspond with each other.
3: Sequence | Sequence Definition: An ordered list of numbers\ | Contrast: Sequence is just a list, a series is the sum of the numbers in the list
4: Recursive Formula | Recursive Definition: Defines the terms in a sequence by relating each term to the ones before it. | Compare: Both express terms in a sequence; Both use computation.
5: Explicit Formula | Explicit Definition: Expresses the Nth term of a sequence in terms of n. | Contrast: Recursive computates all previous numbers; Explicit can computate any number.
6: Arithmetic | Definition: The use of addition is constant throughout. The constant is the common difference. | Compare: Both have a constant between each term.
7: Geometric | Definition: Ratio of consecutive terms is a constant. Constant also called the common ratio. | Contrast: Arithmetic has a constant difference; geometric has a constant ratio.
8: Divergent Definition: An infinite geometric series diverges when IrI>1(or equal to), where "r" is the common ration of the related sequence. | Divergent | Compare: Both are a list of numbers and they describe the series limit.
9: v | Convergent Definition: Infinite geometric series converges when IrI>1, r is the common ration of the related sequence. | Convergent | Contrast: Divergent does not have a limit on the series or sequence. Convergent has a limit that is a real number, if it has a limit then it converges.
10: EXAMPLES | Series: 1 + 3 + 5 + 7 + 9 = 25 | Sequence: 3,8,13,18, 23,28,33,38.. | Recursive Formula: The recursive formula for the sequence 5, 20, 80, 320, ... is an = 4 an-1. | Explicit Formula: an = a1 + (n – 1)d
11: Arithmetic: | Geometric: | Diverges- IrI > 1 Converges- IrI < 1
12: Graphic organizer: Series and Sequences | Series: The sum of the terms of a sequence | Sequence: an ordered list of numbers | Both: They both correspond with each other
13: Graphic organizer: Recursive and Explicit Formula | Recursive: computes all previous numbers in a sequence | Explicit: can compute any number in the sequence | Both: They both use computation; both express terms in a sequence
14: Graphic Organizer: Arithmetic and Geometric | Geometric: Has a constant ratio | Both: Both have constants between each term. | Arithmetic: Use of addition is constant throughout; has a constant difference
15: Graphic Organizer: Divergent and Convergent | Convergent: Has limit that is a real number | Both: both are a list of numbers and describe the series limit | Divergent: Doesn't have a limit on the series or sequence
16: Works Cited Kennedy and Charles, (2004) Algebra 2, Pearson Education Publisher, Upper Saddle River, New Jersey. Mathwords. (n.d.). Retrieved from http://www.mathwords.com Purplemath. (n.d.). Retrieved from http://www.purplemath.com