Find the 61st term of the arithmetic sequence -12, -28, -44, …−12,−28,−44,…

Question

Find the 61st term of the arithmetic sequence -12, -28, -44, …−12,−28,−44,…

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Melanie 3 months 2022-02-19T05:23:41+00:00 2 Answers 0 views 0

Answers ( )

    0
    2022-02-19T05:25:07+00:00

    Answer:

    -972 is the answer

    Step-by-step explanation:

    0
    2022-02-19T05:25:30+00:00

    The 61st term of sequence is -972

    Solution:

    Given arithmetic sequence is:

    -12, -28, -44,  ..

    Let us find the common difference between the successive term and its previous term

    -28 – (-12) = -28 + 12 = -16

    -44 – (-28) = -44 + 28 = -16

    Thus the difference between the terms remains constant

    This is a arithmetic sequence

    The nth term of arithmetic sequence is given by formula:

    [tex]a_n = a_1 + (n-1)d[/tex]

    Where,

    [tex]a_n[/tex] is the nth term of sequence

    [tex]a_1[/tex] is the first term of sequence

    d is the common difference between terms

    In given sequence, -12, -28, -44

    [tex]a_1 = -12\\\\d = -16[/tex]

    Substituting the values in formula,

    [tex]a_n = -12+(n-1)(-16)\\\\a_n = -12 -16n + 16\\\\a_n = 4-16n[/tex]

    To find the 61st term , substitute n = 61

    [tex]a_{61} = 4 – 16 \times 61\\\\a_{61} = 4 – 976\\\\a_{61} = -972[/tex]

    Thus, the 61st term of sequence is -972

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45:7+7-4:2-5:5*4+35:2 =? ( )