Consider the sequence: 8, 11, 14, 17, 20, 23, 26, -. Write a recursive definition: Group of answer choices LaTeX: a_n=2\c

Question

Consider the sequence: 8, 11, 14, 17, 20, 23, 26, ….. Write a recursive definition: Group of answer choices
LaTeX: a_n=2\cdot a_{n-1}-5 a n = 2 ⋅ a n − 1 − 5
LaTeX: a_n=3\cdot a_{n-1} a n = 3 ⋅ a n − 1
LaTeX: a_n=3+a_{n-1} a n = 3 + a n − 1
LaTeX: a_n=8+3\cdot a_{n-1}

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Peyton 2 weeks 2021-10-12T10:07:57+00:00 1 Answer 0

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    2021-10-12T10:09:17+00:00

    Consider the sequence: 8, 11, 14, 17, 20, 23, 26, The recursive definition is a_{n}=3+a_{n-1}

    Solution:

    The given sequence is :- 8, 11, 14, 17, 20, 23, 26, …..

    \text { The first term is } a_{1}=8

    Second term is a_2 = 11 and so on

    On analyzing the above series we can say  

    Each time we want a new term, we add on 3 to previous term which is as follows:-

    8 + 3 = 11

    11 + 3 = 14

    14 + 3 = 17

    17 + 3 = 20

    20 + 3 = 23

    23 + 3 = 26

    And so on

    This recursive step of adding on 3 to the prior term is written in the following general form:

    a_{n}=3+a_{n-1}

    Let’s check the above recursive definition by substituting n = 2 we should get 11

    a_2 = 3 + a_{2-1}\\\\a_2 = 3 + a_{1}\\\\a_2 = 3 + 8 = 11

    Thus the required recursive definition is found

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