SIGMA NOTATIONMrs. Aldous, Mr. Beetz & Mr. ThauvetteDP SL Mathematics

You should be able to…

Express a series using sigma notation. Expand and evaluate an expression

written in sigma notation.

A Greek letter - in maths it translates as “the sum of”

start term r=1

end term r=5

the sum of the first 5 terms

What type of series is it?

Make r=1, r=2, ....

r=1, 4-1=3

r=2, 8-1=7r=3, 12-1=11

3, 7, 11, ....

AP: u1=3, d=4, n=5

=55

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

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

Question

(a) Write down the first three terms of the sequence

Question continued…

(b) Find

(i)

Question continued…

(ii)

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,

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

Be Prepared

Both arithmetic and geometric series can be expressed using sigma notation