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anonymous

  • one year ago

Generate the first 5 terms of this sequence: f(1) = 2 and f(2) = 3, f(n) = f(n - 1) + f(n - 2), for n > 2. A. 2, 3, 5, 7, 9 B. 2, 3, 4, 7, 11 C. 2, 3, 5, 9, 11 D. 2, 3, 5, 8, 13

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  1. SolomonZelman
    • one year ago
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    Ok, so we got a fibonacci here

  2. SolomonZelman
    • one year ago
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    You are already given the first two terms, \(a_1=2\) \(a_2=3\) I am changing my notation, mam, if you don't mind.... (do you?)

  3. anonymous
    • one year ago
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    D

  4. anonymous
    • one year ago
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    i dont mind and thnx zupari :)

  5. SolomonZelman
    • one year ago
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    You are given that: \(\large\color{black}{ \displaystyle a_n=a_{n-1}+a_{n-2} }\) (i.e. every Nth term is going to be equal (or given by) the sum of the 2 terms before it)

  6. SolomonZelman
    • one year ago
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    So, we can use this for 3rd, 4th and 5th terms

  7. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle a_3=a_{2}+a_{1}=3+2=5 }\)

  8. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle a_4=a_{3}+a_{2}=5+3=8 }\)

  9. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle a_5=a_{4}+a_{3}=8+5=13 }\)

  10. SolomonZelman
    • one year ago
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    lets look at it entirely. \(\large\color{black}{ \displaystyle 2,~3,~5,~8,~13 }\)

  11. SolomonZelman
    • one year ago
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    So can see just by looking how every term (from 3rd term and on) has a value same as the sum of the 3 terms before it)

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