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Algebra II Recipe: Arithmetic Series
A. Definition
B. Finding the sum of the first n terms of an arithmetic sequence
  1. Use  is the sum of the first n terms.
  2. Write a rule for the nth term using the a1 and d values.
  3. Find the nth term by substituting the value of n into the rule.
  4. Substitute the n, a1, and an values into  to find the sum.
C. Finding n when Sn is known
  1. Substitute the sum for Sn.
  2. Substitute the first term for a1.
  3. Substitute the rule for an.
  4. Solve for n.
    • If you get a quadratic equation, solve by factoring or the quadratic formula.
    • Choose the positive value.


ExamplesExamples:
Consider the arithmetic series 4 + 7 + 10 + 13 + 16 + 19 + …
Find the sum of the first 30 terms (n = 30).

Consider the arithmetic series 4 + 7 + 10 + 13 + 16 + 19 + …
Find n when Sn = 175.




G Redden

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