Mathematics

Question

(Algebra II) Write a recursive formula for the sequence 5, 18, 31, 44, 57, … Then find the next term.

+13 The next term is 70.
+13 The next term is 83.
-13 The next term is 70.
-13 The next term is 70.

2 Answer

  • The first sentence is correct.

    Please vote my answer branliest! Thanks.
  • Answer:

    Option 1 is correct.

    Recursive formula - [tex]a_n=a_{n-1}+13[/tex] where  [tex]a_1=5[/tex]

    The next term is 70    

    Step-by-step explanation:

    Given : The sequence 5, 18, 31, 44, 57, …              

    To find : The recursive formula and then find the next term.

    Solution :

    First we determine the terms

    First term  [tex]a_1=5[/tex]

    We see that the common difference in the sequence is 18-5=31-18..=13

    So, d=13

    The recursive formula of the sequence is

    [tex]a_n=a_{n-1}+13[/tex] where  [tex]a_1=5[/tex]

    satisfying the sequence 5, 18, 31, 44, 57, …      

    Now, to find 6th term of the sequence put n=6

    [tex]a_n=a_{n-1}+13[/tex]

    [tex]a_6=a_{6-1}+13[/tex]

    [tex]a_6=a_{5}+13[/tex]

    [tex]a_6=57+13[/tex]

    [tex]a_6=70[/tex]

    Therefore, Option 1 is correct. The next term is 70.

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