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Mathematics time 3.

Education 3 days ago
  • User
    Wise Man
    3 days ago

    Solved Examples on sequences and Series. 

     

    Sequence Examples1.

    Arithmetic Sequence: Find the next term in the sequence 2, 5, 8, 11, 14, ...

     

    SOLUTION: The common difference d is  T2–T1 = 5–2=3, 

    Next term from the sequence should be the 6th term  T6. 

    T6 = a + 5d = 2 + 5•3 =15+2=17 answer. 

     

    2. Geometric Sequence: Find the next term in the sequence 2, 6, 18, ...

     

    SOLUTION: The common ratio is T2÷T1 = 6÷2 = 3,

    so the next term is should be T4. 

    T4 = a•r³ = 2 • 3³ =2•27=54. 

    T4 =54 answer. 

     

    Series Examples

    1. Arithmetic Series: Find the sum of the first 5 terms of the sequence 2, 5, 8, ...

    SOLUTION : sum of 1st nth terms of AP =N/2[2a + (n–1)d]

    = 5/2[2•2 +(5–1)•3]

    =2.5(4+4•3)=2.5(4+12)

    =2.5(16)=40. 

    See you in the next class. 

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