Question

Use set-builder notation to write the following sets whose elements are terms of arithmetic sequence

A. (2,4,6,8,10,.....)
B. ( 1,3,5,7,....)

Answer 1

A.
`\text{Set builder}=\{2x:x\in Z,x>0\}`

B.
`\text{Set builder}=\{2x-1:x\in Z,x>0\}`

Explanation:

Set builder form is a form that defines the domain.

A.

The given arithmetic sequence is

2,4,6,8,10,.....

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.

`\text{Set builder}=\{2x:x\in Z,x>0\}`

Therefore the set builder form of given elements is
`\{2x:x\in Z,x>0\}`.

B.

The given arithmetic sequence is

1,3,5,7,....

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.

`\text{Set builder}=\{2x-1:x\in Z,x>0\}`

Therefore the set builder form of given elements is
`\{2x-1:x\in Z,x>0\}`.