1. ARITHMETIC SEQUENCES AND SERIES Week Commencing Monday 12 th October Learning Intention: To be able to find the sum of a series from Sigma (Σ) notation Contents: 1.What is Sigma Notation?What is Sigma Notation? 2.Evaluating a Sum Shown in Sigma NotationEvaluating a Sum Shown in Sigma Notation 3.Sigma Notation and the Sum FormulaSigma Notation and the Sum Formula 4.Assignment 5Assignment 5

2. ARITHMETIC SEQUENCES AND SERIES What is Sigma Notation? Σ is the greek symbol for S. It is pronounced Sigma. In maths Σ stands for “sum”. Therefore,

3. ARITHMETIC SEQUENCES AND SERIES Evaluating a Sum shown in Sigma Notation Example: Evaluate Solution: Substitute r = 1,2, 3, 4, 5 into (2r – 1) to get the first 5 terms: = 1 + 3 + 5 + 7 + 9 = 25

4. ARITHMETIC SEQUENCES AND SERIES Evaluating a Sum shown in Sigma Notation Example: Evaluate Solution: Substitute r = 2, 3, 4, 5 into (4 – 2r) to get the required terms: = 1 + -1 + -3 + -5 = -8 Note: The number of required terms for the sum is 4 i.e (5 – 2) + 1. This method of finding the number of terms for the sum works for all sums of this type.

5. ARITHMETIC SEQUENCES AND SERIES Evaluating a Sum shown in Sigma Notation If the sum involves more than 5 terms we can work out the first term, the common difference, the number of terms and then use the sum formula Example: Evaluate Solution: Substitute r = 1, 2, 3, into (10 – r) to get the first term and to work out the common difference: r = 1: 9r = 2: 8r = 3: 7 Therefore, a = 9, d = -1 and n = 40

6. ARITHMETIC SEQUENCES AND SERIES Assignment 5 – Sigma Notation Follow the link for Assignment 5 on Sigma Notation in the Moodle Course Area. Completed assignments must be submitted by 5:00pm on Monday 19 th October.