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

Name Date

Geometric series Problem set B

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

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 each sum.

    1. (a) 3 + 12 + 48 + … (7 terms)
    2. (b) 4 − 12 + 36 − … (6 terms)
    3. (c) 160 + 80 + 40 + … (10 terms), to 3 significant figures

  2. A geometric series has common ratio 3, and the sum of its first 5 terms is 484. Find the first term.

  3. How many terms of 2 + 10 + 50 + … are needed for the sum to first exceed 20 000?

In context

  1. A rumour reaches 3 people. Each of them passes it to 4 new people, and so on. How many people have heard it after 5 rounds?

  2. A charity raises €12 000 in its first year, and each year it raises 5% more than the year before. Find the total raised in the first 9 years.

  3. A basketball is dropped from a height of 3 m. After each bounce it rises to 80% of the height it fell from. Find the total distance it has travelled when it hits the ground for the 5th time.

  4. A fund-raising page receives $2 on day 1. Each day it receives double the amount of the day before. On which day does the total raised first pass $50 000?

Stretch

  1. The sum of the first \(n\) terms of a geometric series is \(S_n = 3(4^n - 1)\). Find the first term, the common ratio and the 6th term.

jmaths.xyz · AI SL · 12.1.5 Geometric Series