MATH SOLVE

3 months ago

Q:
# Use set-builder notation to write the following sets whose elements are terms of arithmetic sequenceA. (2,4,6,8,10,.....)B. ( 1,3,5,7,....)

Accepted Solution

A:

Answer:A. [tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]B. [tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]Step-by-step explanation:Set builder form is a form that defines the domain.A.The given arithmetic sequence is2,4,6,8,10,.....Here all terms are even numbers. The first term is 2 and the common difference is 2.All the elements are multiple of 2. So, the elements are defined as 2x where x is a non zero positive integer.The set of all 2x such that x is an integer greater than 0.[tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]Therefore the set builder form of given elements is [tex]\{2x:x\in Z,x>0\}[/tex].B.The given arithmetic sequence is1,3,5,7,....Here all terms are odd numbers. The first term is 1 and the common difference is 2.All the elements are 1 less than twice of an integer. So, the elements are defined as 2x-1 where x is a non zero positive integer.The set of all 2x-1 such that x is an integer greater than 0.[tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]Therefore the set builder form of given elements is [tex]\{2x-1:x\in Z,x>0\}[/tex].