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18 July, 09:39

What is the rule for the sequence with the first four terms below?

0.5, 0.25, 0, - 0.25

f (x) = 0.75 minus 0.25 x

f (x) = 0.5 minus 0.25 x

f (x) = 0.75 (negative 0.25) Superscript x

f (x) = 0.5 (0.25) Superscript x

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  1. 18 July, 10:02
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    Answer: f (x) = 0.75 minus 0.25x

    Step-by-step explanation:

    In an arithmetic sequence, the consecutive terms differ by a common difference.

    The formula for determining the nth term of an arithmetic sequence is expressed as

    an = a1 + (n - 1) d

    Where

    a1 represents the first term of the sequence.

    d represents the common difference.

    n represents the number of terms in the sequence.

    From the information given,

    a1 = 0.5

    d = 0.25 - 0.5 = - 0.25

    n = 25

    The rule for the sequence is

    an = 0.5 + (n - 1) - 0.25

    an = 0.5 - 0.25n + 0.25

    an = 0.5 + 0.25 - 0.25n

    an = 0.75 - 0.25n

    Substituting f (x) for an and x for n, it becomes

    f (x) = 0.75 - 0.25x
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