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    IB Math AASL
    /
    Sequences & Series
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    Video

    Video Reviews

    Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Sequences & Series

    Video Reviews

    Watch comprehensive video reviews for Sequences & Series, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    Not your average video:

    Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.

    Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.

    Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.

    SequencesSeriesPaper 1 ProblemsFinancePaper 2 Problems

    The video will automatically pause when it reaches a problem.

    Calculating arithmetic series

    SL Core 1.2

    The sum of the first n terms in an arithmetic sequence is given by

    Sn​=2n​(2u1​+(n−1)d)📖

    or equivalently

    Sn​=2n​(u1​+un​)📖


    Let's say you have the series 1+2+3+⋯+1000.

    1+2+3+⋮500+​1000999998⋮501​→1001→1001→1001→1001→1001​⎭⎪⎪⎪⎪⎬⎪⎪⎪⎪⎫​500 times


    So the sum is 1001⋅500=500500.



    In general, we have:

    u1​+u1​+d+u1​+2d+⋮u1​+2n​d+​un​un​−dun​−2d⋮un​−2n​d​→u1​+un​→u1​+un​→u1​+un​→u1​+un​→u1​+un​​⎭⎪⎪⎪⎪⎬⎪⎪⎪⎪⎫​2n​ times


    which gives the second formula Sn​=2n​(u1​+un​).


    Example

    Find the sum of the first 10 terms in the sequence 1,4,7…


    We have u1​=1, d=3 and n=10 so

    Sn​=210​(2+9⋅3)=145

    Calculating arithmetic series

    SL Core 1.2

    The sum of the first n terms in an arithmetic sequence is given by

    Sn​=2n​(2u1​+(n−1)d)📖

    or equivalently

    Sn​=2n​(u1​+un​)📖


    Let's say you have the series 1+2+3+⋯+1000.

    1+2+3+⋮500+​1000999998⋮501​→1001→1001→1001→1001→1001​⎭⎪⎪⎪⎪⎬⎪⎪⎪⎪⎫​500 times


    So the sum is 1001⋅500=500500.



    In general, we have:

    u1​+u1​+d+u1​+2d+⋮u1​+2n​d+​un​un​−dun​−2d⋮un​−2n​d​→u1​+un​→u1​+un​→u1​+un​→u1​+un​→u1​+un​​⎭⎪⎪⎪⎪⎬⎪⎪⎪⎪⎫​2n​ times


    which gives the second formula Sn​=2n​(u1​+un​).


    Example

    Find the sum of the first 10 terms in the sequence 1,4,7…


    We have u1​=1, d=3 and n=10 so

    Sn​=210​(2+9⋅3)=145
    SequencesSeriesPaper 1 ProblemsFinancePaper 2 Problems