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  • Perplex
    IB Math AIHL
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    Sequences & Series
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    Problems

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    Problem Bank - Sequences & Series

    Access custom-built, exam-style problems for sequences & series. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    Ask Plex AI about problem 29

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    IB: 6
    29

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    When Grace was born in 2007, her parents deposited $10000 into an investment account with an annual interest rate of 5%, compounded quarterly.

    1. Calculate the amount of money in her account when she turns 18.

      [2]

    Once she turns 18, Grace begins depositing $400 into the same account at the end of each month.

    1. Determine the first year in which Grace will have more than $200000 in her account.

      [4]
    30

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    Lucia, an aspiring culinary celebrity, takes out a loan from her bank to purchase equipment for her bakery. The bank agrees to lend her $100,000 at an interest rate of 6% compounded monthly.


    The bank requires equal monthly repayments of $R for 10 years.

    1. Calculate the value of $R to two decimal places.

      [2]

    For the first three years, Lucia makes all her payments on time. At this point she receives a large inheritance and decides to clear the remaining debt with one final lump-sum payment of $X.

    1. Determine the value of $X to two decimal places.

      [2]
    2. Find the amount of interest Lucia saves by making her lump-sum payment at the end of year 3 instead of paying off the loan over 10 years.

      [4]
    31

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    A line segment of 6m is divided into an infinite number of smaller segments. The segments form a geometric sequence with segment lengths k, k2, k3…

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    1. Find the value of k.

      [3]

    An infinite sequence of squares with side lengths k, k2, k3… are arranged side by side on the x-axis starting at the origin.

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    1. Find the combined area of all the squares.

      [4]

    The line L passes through all the squares, dividing them into 2 regions of equal area.

    1. Find the equation of L in the form y=mx+c.

      [5]
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    34
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