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IB Mathematics: Applications and Interpretation SL · 12.1: Sequences & Series · 12.1.3

Name Date

Geometric sequences Problem set B

Work in your exercise book. Use brackets for a negative ratio on the calculator.

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) \(u_1 = 4,\ r = 3\). Find \(u_8\).
    2. (b) 7, −14, 28, … Find \(u_7\).
    3. (c) 72, 36, 18, … Find \(u_7\).

  2. Find the common ratio and the first term.

    1. (a) \(u_2 = 12,\ u_5 = 768\)
    2. (b) \(u_3 = 18,\ u_5 = 162\)

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

    1. (a) 2, 10, 50, …
    2. (b) 81, 27, 9, …

  4. Answer each part.

    1. (a) How many terms are in the sequence 5, 15, 45, …, 10 935?
    2. (b) Find the first term of 2, 6, 18, … that is greater than 10 000.

In context

  1. A basketball is dropped from 5 m. After each bounce it rises to 60% of the height before. Find the height it reaches after the 4th bounce.

  2. A village of 6500 people grows by 3.5% each year. (a) Estimate the population after 9 years. (b) After how many whole years does it first pass 10 000?

  3. A tractor bought for $45 000 loses 15% of its value each year. Find its value after 5 years.

  4. A machine is bought for $60 000 and loses 18% of its value each year. (a) Find its value after 2 years. (b) After how many complete years is it first worth less than half of its original price?

Stretch

  1. \(x,\ x + 6\) and \(x + 24\) are three consecutive terms of a geometric sequence. Find \(x\) and the common ratio.

jmaths.xyz · AI SL · 12.1.3 Geometric Sequences