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

Name Date

Geometric sequences Problem set A

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

Difficulty: first skills applying them stretch

Skills

  1. Find the term asked for.

    1. (a) \(u_1 = 3,\ r = 2\). Find \(u_{10}\).
    2. (b) 4, −12, 36, … Find \(u_7\).
    3. (c) 80, 40, 20, … Find \(u_9\).

  2. Find the common ratio and the first term.

    1. (a) \(u_2 = 6,\ u_5 = 162\)
    2. (b) \(u_3 = 20,\ u_5 = 80\)

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

    1. (a) 5, 15, 45, …
    2. (b) 64, 32, 16, …

  4. Answer each part.

    1. (a) How many terms are in the sequence 7, 14, 28, …, 3584?
    2. (b) Find the first term of 3, 12, 48, … that is greater than 10 000.

In context

  1. A ball is dropped from 2 m. After each bounce it rises to 70% of the height before. Find the height it reaches after the 5th bounce.

  2. A town of 42 000 people grows by 2.5% each year. (a) Estimate the population after 8 years. (b) After how many whole years does it first pass 60 000?

  3. A van bought for £18 000 loses 12% of its value each year. Find its value after 6 years.

  4. A car is bought for £25 000 and loses 15% of its value each year. (a) Find its value after 3 years. (b) After how many complete years is it first worth less than half of its original price?

Stretch

  1. \(x,\ x + 4\) and \(x + 12\) are three consecutive terms of a geometric sequence. Find \(x\) and the common ratio.

jmaths.xyz · AI SL · 12.1.3 Geometric Sequences