Write a recursive rule an explicit rule for the arithmetic sequence 15,22.5,30,37.5

Question

Write a recursive rule an explicit rule for the arithmetic sequence 15,22.5,30,37.5

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Autumn 2 hours 2021-10-13T03:49:00+00:00 1 Answer 0

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    2021-10-13T03:50:12+00:00

    Answer:

    a_n = a_o +(n-1) d

     22.5 = 15 +(2-1) d

     d = 22.5-15 =7.5

    The general expression is:

     a_n = 15+ (n-1)*7.5 , n \geq 1

    Step-by-step explanation:

    For this case we have the following arithmetic sequence given:

    15, 22.5, 30,37.5

    In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:

    a_n = a_o +(n-1) d

    Where a_n is the nth term a_o the initial value for the sequence and d the common difference. For this case we have that a_o =15

    And for the first term we have:

     15= 15 +(1-1)d

    For the second term we have this:

     22.5 = 15 +(2-1) d

    And solving for the value of d we got:

     d = 22.5-15 =7.5

    And for the 3th term we have:

     a_3= 15 +(3-1)*7.5 =30

    And for the 4th term

    a_4 =15 +(4-1)*7.5 =37.5

    So then our expression is correct and would be given by:

     a_n = 15+ (n-1)*7.5 , n \geq 1

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