Question

Compare and contrast the following in details 

a. An arithmetic sequence and a geometric sequence.

b. A sequence and a series.

c. Discrete data and continuous data.

d. An explicit and a recursive representation.

https://gyazo.com/ab539bf1947386c5069ceebc85f0e8e8 

Answer 1

a. Differences & Similarities between arithmetic and geometric sequences:

The differences between arithmetic and geometric sequences is that arithmetic sequences follow terms by adding, while geometric sequences follow terms by multiplying.

The similarities between arithmetic and geometric sequences is that they both follow a certain term pattern that can't be broken.

Geometric sequence's are sequences that are found by multiplying the previous term by a constant. For examples (2,4,8,_,_,_) (9,18,36,_,_,_) (24,48,96,_,_,_) (13,26,52,_,_,_) (8,16,32,_,_,_)

An Arithmetic Sequence is when there is one term, and the next term follows that same sequence. For example,  (3,6,9_,_,_) (2,4,6,_,_,_) (10,20,30,_,_,_) (12,24,36,_,_,_) (20,40,60,_,_,_)

b. Difference and similarity between sequence and series:

The list of numbers written in a definite order is called a sequence. The sum of terms of an infinite sequence is called an infinite series. A sequence can be defined as a function whose domain is the set of Natural numbers. Therefore sequence is an ordered list of numbers and series is the sum of a list of numbers. Example of a sequence: 2, 4, 6, 8, 10 … Now if we add them up: 2+4+8+10+ … This is a series.

The sequence is defined as the collection of numbers or objects that follow a definite pattern. When the elements of the sequence are added together, they are known as series.

c. Comparison between discrete data and continuous data:

Discrete - Discrete data is one that has clear spaces between values, countable, It can take only distinct or separate values, graphical representation is bar graph, Tabulation is known as Ungrouped frequency distribution,Example- Days of the week.

Continuous - Continuous data is one that falls on a continuous sequence, measurable, It can take any value in some interval, graphical representation is histogram, Tabulation is known as Grouped frequency distribution, Example- Market price of a product