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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.

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    13 / 53 problems visible - Upgrade to view all problems

    IB: 4
    1

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    0 / 7

    Quinn takes out a loan of $350,000 to purchase a small condo in Boston. The bank agrees to lend to him at an 8% annual interest rate, compounded monthly.


    To repay the loan, Quinn makes monthly payments of $P over 15 years.

    1. Determine the value of P to the nearest dollar.

      [3]
    2. Calculate the total payments Quinn makes to the bank.

      [2]
    3. Hence find the total interest paid by Quinn.

      [2]
    2

    !

    0 / 9

    Jacob is choosing between two ways to save up for a vacation planned 7 years from now. He is considering two different strategies to save a total of €Q for his vacation.

    • Option A: Deposit €4000 today in an account that earns 4.2% annual interest, compounded monthly.

    • Option B: Deposit €P at the end of each month until the vacation in an account that earns 5% annual interest, compounded monthly.

    1. Calculate, to the nearest euro, the value of €Q.

      [3]
    2. Find the value of P, giving your answer to two decimal places.

      [3]
    3. Determine which option yields greater total interest, and state by how much.

      [3]
    3

    0 / 6

    An arithmetic sequence has 2u6​=S6​=5, where S6​ is the sum of the first 6 terms. Find the second term, u2​, of the sequence.

    [6]
    4

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    An arithmetic sequence has u3​=5 and u7​=−7.

    1. Find the common difference d and the first term u1​ of the sequence.

      [3]
    2. Hence find u10​.

      [1]
    3. Find S10​.

      [2]
    5

    0 / 5

    A geometric sequence has u3​=3 and u6​=98​. Find S∞​ for this sequence.

    [5]
    6

    0 / 6

    Ella invests $500 in a savings account that earns 4% interest per annum, compounded quarterly.

    1. Find an expression for the balance of Ella's savings after n years.

      [2]
    2. Calculate the value of Ella's savings after 12 years. Give your answer to the nearest dollar.

      [2]

    Ella wants to purchase a racing bike for $700.

    1. Find the number of years after which her savings will be sufficient to purchase the bike.

      [2]
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