Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77-99,100.​

Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77….99,100.​

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  1. Answer:

    The sum is 2275

    Step-by-step explanation:

    Given

    [tex]75,76,77….99,100[/tex]

    Required

    The sum

    Using arithmetic progression, we have:

    [tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

    Where:

    [tex]T_1 = 75[/tex] — first term

    [tex]T_n = 100[/tex] — last term

    [tex]n = T_n – T_1 + 1[/tex]

    [tex]n = 100 – 75 + 1 = 26[/tex]

    So, we have:

    [tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

    [tex]S_n = \frac{26}{2}*(75 + 100)[/tex]

    [tex]S_n = 13*175[/tex]

    [tex]S_n = 2275[/tex]

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