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IB Mathematics: Applications and Interpretation HL · 12.1: Sequences & Series · 12.1.5

Name Date

Geometric series Problem set A

Work in your exercise book. Decide first whether you need a term or a sum.

Difficulty: first skills applying them stretch

Skills

  1. Find each sum.

    1. (a) 2 + 6 + 18 + … (8 terms)
    2. (b) 5 − 10 + 20 − … (10 terms)
    3. (c) 100 + 50 + 25 + … (12 terms), to 3 significant figures

  2. A geometric series has common ratio 2, and the sum of its first 6 terms is 315. Find the first term.

  3. How many terms of 4 + 12 + 36 + … are needed for the sum to first exceed 10 000?

In context

  1. A message is sent to 4 people. Each of them sends it to 3 new people, and so on. How many people have received it after 6 rounds?

  2. A starting salary is $28 000 and it rises by 3% each year. Find the total earned in the first 10 years.

  3. A ball is dropped from a height of 5 m. After each bounce it rises to 60% of the height it fell from. Find the total distance the ball has travelled when it hits the ground for the 6th time.

  4. A challenge asks you to save £3 on day 1 and to save double the amount of the day before on each following day. On which day does the total first pass £10 000?

Stretch

  1. The sum of the first \(n\) terms of a geometric series is \(S_n = 5(2^n - 1)\). Find the first term, the common ratio and the 6th term.

jmaths.xyz · AI HL · 12.1.5 Geometric Series