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

Name Date

Arithmetic sequences Problem set B

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

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. Find the term asked for.

    1. (a) \(u_1 = 11,\ d = 7\). Find \(u_{14}\).
    2. (b) 70, 63, 56, … Find \(u_{18}\).
    3. (c) 1.5, 4, 6.5, … Find \(u_{27}\).

  2. The 5th term of an arithmetic sequence is 19 and the 11th term is 43. Find the first term and the common difference.

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

    1. (a) 9, 15, 21, …
    2. (b) 50, 45, 40, …
    3. (c) −9, −5, −1, …

  4. Answer each part.

    1. (a) Which term of 3, 11, 19, … is equal to 235?
    2. (b) Find the first negative term of 92, 87, 82, …

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

    1. (a) \(u_3 = 37,\ u_9 = 7\)
    2. (b) \(u_7 = 16,\ u_{17} = 56\); find \(u_{32}\)

  6. Say which of these numbers are terms of the sequence 8, 14, 20, 26, …, and give the position of each one that is.

    1. (a) 302
    2. (b) 305
    3. (c) 164

In context

  1. A garden is planted in rows. The first row has 14 plants and each row has 2 more plants than the row before. (a) How many plants are in row 18? (b) Which row has 60 plants?

  2. A water tank holds 80 litres and loses 2.5 litres every minute. (a) Write an expression for the volume after \(n\) minutes. (b) How long until it is empty?

  3. Tiles are laid in a row and edged with strips. One tile needs 6 strips, two tiles need 10 strips and three tiles need 14 strips. (a) How many strips are needed to edge a row of 18 tiles? (b) A shop has 155 strips. What is the greatest number of tiles it can edge in one row?

Stretch

  1. \(x,\ 3x + 1\) and \(6x - 5\) are three consecutive terms of an arithmetic sequence. Find \(x\) and the three terms.

  2. How many multiples of 9 are there between 200 and 600?

jmaths.xyz · AI HL · 12.1.1 Arithmetic Sequences