Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/sequences-series/12-1-4/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · 12.1: Sequences & Series · 12.1.4

Name Date

Sigma notation Problem set B

Work in your exercise book. Write out the first three terms before you start.

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. Evaluate each sum.

    1. (a) \(\displaystyle\sum_{r=1}^{7}(3r + 2)\)
    2. (b) \(\displaystyle\sum_{r=4}^{12}(5r - 3)\)
    3. (c) \(\displaystyle\sum_{r=1}^{6} 3 \times 2^r\)
    4. (d) \(\displaystyle\sum_{k=0}^{5} 4 \times 3^k\)

  2. How many terms are there in \(\displaystyle\sum_{r=7}^{52} u_r\)?

  3. Write each series in sigma notation.

    1. (a) 4 + 7 + 10 + … + 97
    2. (b) 5 + 15 + 45 + … + 3645

  4. Say whether \(\displaystyle\sum_{r=1}^{26}(120 - 4r)\) is arithmetic or geometric, and evaluate it.

  5. Evaluate each sum.

    1. (a) \(\displaystyle\sum_{r=1}^{25} 8\)
    2. (b) \(\displaystyle\sum_{r=0}^{4} 3\times(-2)^r\)

Stretch

  1. Given that \(\displaystyle\sum_{r=1}^{n}(2r + 5) = 315\), find \(n\).

  2. \(\text{Find the smallest } n \text{ for which }\displaystyle\sum_{r=1}^{n} 4\times 3^{r-1} > 5000\).

jmaths.xyz · AI HL · 12.1.4 Series & Sigma Notation