Use set-builder notation to write the following sets whose elements are terms of arithmetic sequence A. (2,4,6,8,10,-.)

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,….)

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Julia 1 week 2021-09-09T14:27:56+00:00 1 Answer 0

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    2021-09-09T14:29:38+00:00

    Answer:

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

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

    Step-by-step 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\}.

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