Arithmetic Sequences Sequence is a list of numbers

Arithmetic Sequences Sequence is a list of numbers typically with a pattern. Each number in the list called a term. 2, 4, 6, 8, … a 1, a 2, a 3, a 4, … The first term in a sequence is denoted as a 1, the second term is a 2, and so on up to the nth term an.

Finite Sequence has a fixed number of terms. {2, 4, 6, 8} A sequence that has infinitely many terms is called an infinite sequence. {2, 4, 6, 8, …} Algebraically, a sequence can be written as an explicit formula or as a recursive formula. Explicit formulas show to find a specific term number (n). Recursive formula show to get from a given term (an 1) to the next term (an)

An Arithmetic Sequence is a sequence where you use repeated addition (with same number) to get from one term to the next. Ex: 4, 1, -2, -5, … -3 -3 is an arithmetic sequence -3 The number that needs to be added each time to get to the next term is called the common difference The common difference for the above arithmetic sequence is -3.

First term Common difference For the example: Explicit Formula Substitute the values: an = 4 + (n – 1)(- 3) So the explicit formula is: an = -3 n + 7 Recursive formula for an Arithmetic Sequence: a 1 = # an = an-1 + d 4, 1, -2, -5, … The Recursive Formula is: a 1 = 4 an = an-1 – 3

How do you add these sequences of numbers? A series is the sum of ALL the terms of a sequence. (can be finite or infinite) A partial sum is the sum of the first n terms of a series…denoted Number of terms Sn First term Last term

For the example: 4, 1, -2, -5, … 1) Find S 4. 2) Find S 20. (Think…. )

Example: For the arithmetic sequence 2, 6, 10, 14, 18, … a) Write the explicit formula for the sequence. b) Write the recursive formula for the sequence. c) Find the 15 th partial sum of the sequence (S 15). a 1 = # an = an-1 + d