Arithmetic Sequences

Arithmetic Sequences

1. The nth term of an arithmetic sequence can be found using the explicit formula.

   • Explicit Formula
     • d = common difference
       • Common Difference: The number that is added to get to the next term.
     • n = term number

2. An arithmetic sequence is a list of numbers whose terms all differ by the same non-zero number

3. Example 1: What is the common difference of the following sequence? 3, 11, 19, 27... Take the last term given and subtract the term before it. This will give you the common difference. 27 - 19 = 8, therefore, 8 is the common difference (d).

   • Example 2: In example 1 we found the common difference of the arithmetic sequence 3, 11, 19, 27... to be 8. What is the first term? The first term of the sequence is 3.
     • Example 3: To find the explicit formula we just need the common difference and the first term. Put the first term in for a1 and the common difference in for d. This gives us an=3 + (n -1)(8). We can distribute the 8 to everything in the parenthesis. I like to move the d-value to the front of the parenthesis. an=3+8(n-1). Distributing the 8 we get an = 3 + 8n -8. Combining like terms we get an = 8n - 5.

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