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

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Arithmetic series Problem set B

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

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 + 10 + 17 + … (20 terms)
    2. (b) 50 + 45 + 40 + … (30 terms)
    3. (c) The first 60 even numbers

  2. An arithmetic series has first term 3, and the sum of its first 12 terms is 300. Find the common difference.

  3. Find each sum.

    1. (a) 15 terms, first term 4, last term 88
    2. (b) 2 + 5 + 8 + … + 101

  4. Answer each part.

    1. (a) How many terms of 4 + 10 + 16 + … are needed for the sum to first exceed 690?
    2. (b) The sum of the first \(n\) terms of 5 + 9 + 13 + … is 779. Find \(n\).

  5. The 5th term of an arithmetic series is 23 and the 11th term is 47. Find the sum of the first 14 terms.

In context

  1. Pipes are stacked with 30 in the bottom row and one fewer in each row above. The top row has 11 pipes. How many pipes are there?

  2. Tomas saves €30 in the first month and €4 more each month than the month before. (a) How much has he saved in total after 20 months? (b) In which month does his total first pass €2000?

Stretch

  1. The sum of the first \(n\) terms of a sequence is \(S_n = 4n^2 - n\). Find the first term and a rule for \(u_n\).

  2. Find the sum of the multiples of 9 from 9 to 360.

jmaths.xyz · AI SL · 12.1.2 Arithmetic Series