Summation notation a way to show the operation

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 Variable Lower limit Algebraic expression The 20 th partial sum of the arithmetic sequence: 2, 7, 12, 17, … would be represented as Explicit formula of the sequence

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) 2)

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.

In Class Practice: For each sequence below: a) Determine if it is arithmetic or geometric b) Identify the common difference or ratio c) Write the explicit and recursive formulas for the sequence d) Find the 16 th partial sum of the each sequence 1) a) Geometric b) r = 5 c) E: an = 5 n-1 R: a 1 = 1 an = an-1 ∙ 5 d) 3. 8147 E 10 2) a) Arithmetic b) d = 8 c) E: an = 8 n-42 R: a 1 = -34 an = an-1+8 d) 416