sigma notation

1. sigma notation Mrs. Aldous, Mr. Beetz & Mr. ThauvetteDP SL Mathematics

2. You should be able to… • Express a series using sigma notation. • Expand and evaluate an expression written in sigma notation.

3. A Greek letter - in maths it translates as “the sum of” the sum of the first 5 terms end term r=5 start term r=1 What type of series is it? 3, 7, 11, .... Make r=1, r=2, .... AP: u1=3, d=4, n=5 r=1, 4-1=3 =55 r=2, 8-1=7 r=3, 12-1=11

4. Find the following information: 1. Type of series (AP or GP) 2. n 3. u1 4. difference (d) or ratio (r) 5. The sum 1. 8, 16, 32, .... a GP 2. n=6 (careful .. use your fingers to count) 3. u1 = 8 4. r= 2 5. 504

5. Solve each of the following sums 1. GP: 265680 2. AP: 858 3. GP: 1023 4. GP: 315012 (approx.) 5. AP: 102.5 6. AP: 10400

6. Question (a) Write down the first three terms of the sequence

7. Question continued… (b) Find (i)

8. Question continued… (ii)

9. You should know… • The Greek letter is used to denote the sum of the terms of a series. • To express a series using sigma notation, use the form (general term). For example,

10. GDC • Use the sum and sequence functions to evaluate expressions written in sigma notation. For example, to observe the terms of the arithmetic sequence: and to evaluate its sum, we could use the following

11. Be Prepared • Both arithmetic and geometric series can be expressed using sigma notation