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IB Mathematics: Applications and Interpretation SL · 12.1: Sequences & Series · 12.1.1

Name Date

Arithmetic sequences Problem set A

Work in your exercise book. Write the rule you use each time.

Difficulty: first skills applying them stretch

Skills

  1. Find the term asked for.

    1. (a) \(u_1 = 9,\ d = 6\). Find \(u_{15}\).
    2. (b) 52, 45, 38, … Find \(u_{20}\).
    3. (c) 2.5, 4, 5.5, … Find \(u_{31}\).

  2. The 4th term of an arithmetic sequence is 20 and the 9th term is 45. Find the first term and the common difference.

  3. Write an expression for \(u_n\).

    1. (a) 8, 13, 18, …
    2. (b) 30, 26, 22, …
    3. (c) −7, −4, −1, …

  4. Answer each part.

    1. (a) Which term of 5, 12, 19, … is equal to 187?
    2. (b) Find the first negative term of 80, 77, 74, …

  5. Find \(u_1\) and \(d\), and then the term asked for.

    1. (a) \(u_3 = 31,\ u_{11} = -1\)
    2. (b) \(u_6 = 10,\ u_{15} = 37\); find \(u_{30}\)

  6. Say which of these numbers are terms of the sequence 5, 12, 19, 26, …, and give the position of each one that is.

    1. (a) 306
    2. (b) 310
    3. (c) 152

In context

  1. A theatre has 18 seats in its front row. Each row has 3 more seats than the row in front. (a) How many seats are in row 14? (b) Which row has 90 seats?

  2. A candle is 24 cm tall and burns down 1.5 cm every hour. (a) Write an expression for its height after \(n\) hours. (b) How long does it last?

  3. Square tables are pushed together in a row. One table seats 4 people, two tables seat 6 and three tables seat 8. (a) How many people can sit at a row of 15 tables? (b) A club needs seats for 91 people. How many tables must be in the row?

Stretch

  1. \(x,\ 2x + 3\) and \(5x - 4\) are three consecutive terms of an arithmetic sequence. Find \(x\) and the three terms.

  2. How many multiples of 7 are there between 100 and 500?

jmaths.xyz · AI SL · 12.1.1 Arithmetic Sequences