 Site Navigation                            Algebra II Recipe: Arithmetic Sequences A. Definition
1. sequences - an ordered list of numbers.
2. terms - the numbers in the sequence.(a variable with a subscript number gives the term place in the sequence such as  means the 7th term)
3. general term - denoted by an and is the nth term.
4. arithmetic sequence - a sequence where the difference “d” between consecutive terms is constant.
5. rule - an equation that allows you to find any term in the sequence. B . The Rule for an Arithmetic Sequence: an = a1 + (n - 1)d
1. an is the nth term of the sequence.
2. a1 is the first term of the sequence.
3. n is the number of terms in the sequence.
4. d is the common difference.
5. Use only the a1 and d values to write the rule. C. Writing a Rule When You Are Only Given the Arithmetic Sequence
1. Determine the a1 and d values.
2. Substitute the a1 and d values into an = a1 + (n - 1)d.
3. Simplify the equation.   Example:   Write a rule for the nth term of the arithmetic sequence 50, 44, 38, 32, … D. Writing a Rule When You Know Some Term In the Arithmetic Sequence and the Common Difference.
1. Find a1 by substituting the given information into an = a1 + (n - 1)d.
2. Substitute the a1 and d values only into an = a1 + (n - 1)d.
3. Simplify the equation.   Example:   Write a rule for the nth term of an arithmetic sequence with a13 = 30 and a common difference of 3/2. E. Writing a Rule When You Only Know Two Terms in the Arithmetic Sequence.
1. Write a system of equations.
• Eq. 1: substitute the largest n into an = a1 + (n - 1)d.
• Eq. 2: substitute the smallest n into an = a1 + (n - 1)d.
2. Simplify each equation.
3. Subtract the equations (Eq. 1 - Eq. 2) to find d.
4. Substitute the value of d into Eq. 2 (the "smallest equation") to find a1.
5. Substitute the values of a1 and d into an = a1 + (n - 1)d.
6. Simplify the equation.   Example:   Write a rule for the nth term of an arithmetic sequence when a6 = 10 and a21 = 55.

G Redden

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