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IB Mathematics: Applications and Interpretation SL · 12.1: Sequences & Series · 12.1.6

Name Date

Mixed practice: which model? Problem set A

Work in your exercise book. For each question decide: arithmetic or geometric, a term or a sum.

Difficulty: first skills applying them stretch

Skills

  1. Say whether each sequence is arithmetic, geometric or neither.

    1. (a) 12, 9.5, 7, 4.5, …
    2. (b) 8, 12, 18, 27, …
    3. (c) 1, 4, 9, 16, …
    4. (d) 54, −18, 6, −2, …

  2. An arithmetic sequence has \(u_1 = 5,\ d = 3\). A geometric sequence has \(v_1 = 5,\ r = 1.2\). Find the smallest \(n > 1\) for which \(v_n > u_n\).

  3. £3500 is invested at 4.2% simple interest per year. Find the amount after 5 years.

In context

  1. Two phone plans both cost £500 in the first month of a contract. Plan A goes up by £40 each month. Plan B goes up by 5% each month. In which month does plan B first cost more than plan A?

  2. A plant's height is measured each week: 12.0, 14.1, 15.9, 18.2, 20.0 cm. Model the heights as an arithmetic sequence and predict the height in week 10.

  3. A swimmer does 20 lengths on day 1 and 4 more each day. (a) How many lengths on day 15? (b) How many lengths in total over the 15 days? Say which is a term and which is a sum.

  4. A pattern is made of squares. Stage 1 has 2 squares, stage 2 has 6 squares and stage 3 has 18 squares. (a) Is the number of squares arithmetic or geometric? Give the common difference or ratio. (b) How many squares are in stage 7? (c) How many squares are there in stages 1 to 7 altogether?

jmaths.xyz · AI SL · 12.1.6 Mixed Practice & Exam Prep