Presentation on theme: "C1: Sigma Notation For Sequences Sigma is a Greek letter. Capital sigma looks like this: Σ In Maths this symbol is used to mean ‘sum of’: add together."— Presentation transcript:
C1: Sigma Notation For Sequences Sigma is a Greek letter. Capital sigma looks like this: Σ In Maths this symbol is used to mean ‘sum of’: add together everything indicated. You may have seen the symbol used in Statistics.
C1: Sigma Notation For Sequences There is information around the sigma symbol when it is used to find series. It tells you which terms of the sequence need to be added together. is a typical question. Let’s look at what it all means. 1) The sequence is to the right of sigma. Here the variable is ‘r’ – it can be any letter (though i, k, n and r are common). 2) The first term number of the series is below sigma. This is not necessarily 1! 3) The last term of the series is above sigma. So this question is: Add up the first four terms of the sequence 2 r
C1: Sigma Notation For Sequences Now you know what the notation means, do the question. Example 1: Method 1) Check the notation to understand the terms you need to add for the series. Return to previous slide Return to previous slide 2) Find them and add them together. 2 1 = = = = = 30
C1: Sigma Notation For Sequences Example 2: Potential Clues Check the number of terms. If it’s relatively high, the sequence could be an arithmetic progression. Find the first three terms of the sequence... if they have a common difference, you have an arithmetic progression. If the sequence is an arithmetic progression, you can use the arithmetic progression formulas in the formula booklet. Otherwise, use something else or you will lose marks. Some sigma notation questions are arithmetic progression questions in disguise – like this one!
C1: Sigma Notation For Sequences Example 2: Method 1) Once you know it’s an arithmetic progression, find the value of a by subbing 1 into the sequence formula. a = 3 x 1 – 1 = 2 2) Find l by subbing the final term number (from above sigma). l = 3 x 20 – 1 = 59 3) Use the smaller sum to n terms formula. S 20 = 610
C1: Sigma Notation For Sequences Example 3: Sigma notation can also be about a recurrence relation. Method 1) Check the notation to understand the terms you need to add for the series. 2) Find them and add them together. u 2 = 2 u 3 = 6 u 4 = 22 u 5 = = 117 First term......to fifth term.
C1: Sigma Notation For Sequences Notes Refer to this slide for an explanation of sigma notation.this slide Sigma notation can be used with arithmetic progressions but not all sigma notation questions are arithmetic progressions! Refer to this slide for more details.this slide Equally, sigma notation can be used with recurrence relations. These will use the usual notation (u n+1 and so on). Refer to this slide for more details.this slide