What is the explicit formula for this sequence? -7,-3, 1, 5,… A. an = -7 + (n – 1)(-4) B. an = 9+ (n – 1)(-4)

Question

What is the explicit formula for this sequence?
-7,-3, 1, 5,…

A. an = -7 + (n – 1)(-4)
B. an = 9+ (n – 1)(-4)
C. an = -7 + (n – 114
D. an= -4 + (n – 1)(-7

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Melody 2 weeks 2021-09-12T09:53:57+00:00 1 Answer 0

Answers ( )

    0
    2021-09-12T09:55:42+00:00

    Answer:

    a_n=-7+4(n-1)

    or

    a_n=-7+(n-1)(4)

    Step-by-step explanation:

    -7,-3,1,5,… is a arithmetic sequence.

    Arithmetic sequences have a common difference. That is, it is going up by 4 each time.

    When you see arithmetic sequence, you should think linear equation.

    The point-slope form of a line is y-y_1=m(x-x_1).

    m is the common difference, the slope.

    Any they are using the point at x=1 in the point slope form.  So they are using (1,-7).

    So let’s put this into our point-slope form:

    y-(-7)=4(x-1)

    y+7=4(x-1)

    Subtract 7 on both sides:

    y=-7+4(x-1)

    So your answer is

    a_n=-7+4(n-1)

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