What is the equivalent recursive definition for an = 12+ (n – 1)3? A. a1 = 3, An = An-1 + 12 B. a1 = 12, An = 30n-1 C. a1

Question

What is the equivalent recursive definition for an = 12+ (n – 1)3?
A. a1 = 3, An = An-1 + 12
B. a1 = 12, An = 30n-1
C. a1 = 12, Un = On-1 +3
D. a1 = n, an= 1201-1+3

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Eirian 1 year 2021-09-05T15:12:48+00:00 1 Answers 4 views 0

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    2021-09-05T15:14:45+00:00

    Answer:

    [tex]A_1 = 12[/tex]

    [tex]A_n = A_{n-1} + 3[/tex]

    Step-by-step explanation:

    Given

    [tex]A_n =12+(n-1)3[/tex]

    Required

    Write as recursive

    We have:

    [tex]A_n =12+(n-1)3[/tex]

    Open bracket

    [tex]A_n =12+3n-3[/tex]

    [tex]A_n =12-3+3n[/tex]

    [tex]A_n =9+3n[/tex]

    Calculate few terms

    [tex]A_1 =9+3*1 = 9 + 3 = 12[/tex]

    [tex]A_2 =9+3*2 = 9 + 6 = 15[/tex]

    [tex]A_3 =9+3*3 = 9 + 9 = 18[/tex]

    The above shows that the rule is to add 3.

    So, we have:

    [tex]A_1 = 12[/tex]

    [tex]A_n = A_{n-1} + 3[/tex]

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