The sum of 5 55 consecutive integers is 110 What is the fourth number in this sequence

Question

The sum of
5
55 consecutive integers is
110
What is the fourth number in this sequence

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Serenity 2 weeks 2021-09-13T14:27:06+00:00 1 Answer 0

Answers ( )

    0
    2021-09-13T14:28:31+00:00

    Question:

    The sum of  5  consecutive integers is  110
    . What is the fourth number in this sequence

    Answer:

    The fourth number in this sequence is 23

    Step-by-step explanation:

    Explanation:

    Consecutive numbers  are numbers that come one after another with no numerical gaps. Like these:

    4,
    5
    ,
    6
    ,
    7
    ,
    8  or these  17
    ,
    18,
    19
    ,
    20
    ,
    21

    We need to find 5 consecutive integers that add up to 110.

    Let’s call the first integer in the series  

    N  for  number
    . The next integer will be  

    N
    +
    1  since it is  1 greater  than N
    .

    The next integers will be  N+
    2
    , N
    +
    3  and  N
    +
    4  since they are 2, 3 and 4 greater than  N  respectively.

    N
    +
    (
    N
    +
    1
    )
    +
    (
    N
    +
    2
    )+(
    N
    +
    3
    )
    +
    (
    N
    +
    4
    )
    =
    110

    Now remove parentheses and add like terms:

    N
    +
    N
    +
    1
    +
    N
    +
    2
    +
    N
    +
    3
    +
    N
    +
    4
    =
    110

    5N
    +
    10
    =
    110

    Now finish simplifying:

    5
    N
    +
    10=
    110

    5
    N
    =
    100

    N = \frac{100}{5}


    N
    =
    20

    Since  N
    =
    20

    our 5 consecutive numbers are:

    20
    ,
    21
    ,
    22
    ,
    23
    ,
    24

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