2. The symbol for summation is the Greek letter Sigma, S.
Summation notation: a way to show the operation of adding a series of values related by an algebraic expression or formula.
The symbol for summation is the Greek letter Sigma, S.
Upper limit
Algebraic expression
The 20th partial sum of the arithmetic sequence: 2, 7, 12, 17,… would be represented as
Variable
Lower limit
Explicit formula of the sequence

3. You can still use the partial sum formulas to find the answer to these, but you have to make sure you recognize if the expression represents an arithmetic or geometric sequence.
1) )

4. Formula for the infinite sum
An infinite sum means that you add ALL the terms of infinite sequence.
The only type of infinite sequences that can be added are convergent sequences.
Formula for the infinite sum
of a sequence
Remember this is only used on geometric sequences with fractional value for r.

5. In Class Practice: For each sequence below:
Determine if it is arithmetic or geometric
Identify the common difference or ratio
Write the explicit and recursive formulas for the sequence
Find the 16th partial sum of the each sequence
1) )
Geometric
r = 5
E: an = 5n-1 R: a1 = 1
an = an-1 ∙ 5
d) E 10
Arithmetic
d = 8
E: an = 8n-42 R: a1 = -34
an = an-1+8
d) 416