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IB Mathematics: Applications and Interpretation SL · 12.1: Sequences & Series · 12.1.2

Name Date

Arithmetic series Problem set A

Work in your exercise book. Say which form of the sum you are using.

Difficulty: first skills applying them stretch

Skills

  1. Find each sum.

    1. (a) 4 + 9 + 14 + … (25 terms)
    2. (b) 60 + 54 + 48 + … (30 terms)
    3. (c) The first 50 odd numbers

  2. An arithmetic series has first term 2, and the sum of its first 10 terms is 155. Find the common difference.

  3. Find each sum.

    1. (a) 12 terms, first term 5, last term 71
    2. (b) 3 + 7 + 11 + … + 99

  4. Answer each part.

    1. (a) How many terms of 2 + 6 + 10 + … are needed for the sum to first exceed 800?
    2. (b) The sum of the first \(n\) terms of 7 + 10 + 13 + … is 847. Find \(n\).

  5. The 4th term of an arithmetic series is 19 and the 9th term is 44. Find the sum of the first 15 terms.

In context

  1. Logs are stacked with 24 in the bottom row and one fewer in each row above. The top row has 9 logs. How many logs are there?

  2. Noor saves £20 in the first month and £5 more each month than the month before. (a) How much has she saved in total after 24 months? (b) In which month does her total first pass £3000?

Stretch

  1. The sum of the first \(n\) terms of a sequence is \(S_n = 3n^2 + 2n\). Find the first term and a rule for \(u_n\).

  2. Find the sum of the multiples of 6 from 6 to 300.

jmaths.xyz · AI SL · 12.1.2 Arithmetic Series