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Arithmetic Sequences

Arithmetic Sequences. OBJECTIVES: Determine if a Sequence is Arithmetic Find a Formula for an Arithmetic Sequence Find the Sum of an Arithmetic Sequence. Arithmetic Sequence.

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Arithmetic Sequences

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  1. Arithmetic Sequences OBJECTIVES: Determine if a Sequence is Arithmetic Find a Formula for an Arithmetic Sequence Find the Sum of an Arithmetic Sequence

  2. Arithmetic Sequence • Arithmetic Sequence: a sequence in which each term after the first differs from the preceding term by a constant amount. The difference between consecutive terms is called the common difference of the sequence • Common difference, d, is found by subtracting any term from the term that directly follows. • General Term of an Arithmetic Sequence: the nth term (general term) of an arithmetic sequence with the first term and common difference • Explicit formula: • Recursive formula:

  3. Arithmetic Sequence • EX 1: Find the common difference and write out the first four terms of the arithmetic sequence

  4. Arithmetic Sequence • EX 2: Find the nth term of the arithmetic sequence whose initial term and common difference are given. What is the fifth term?

  5. Arithmetic Sequence • EX 3: Find the eighth term of the arithmetic sequence whose first term is 4 and whose common difference is -7

  6. Arithmetic Sequence • EX 4: Find the first term and the common difference of the arithmetic sequence described. Give an Explicit and Recursive Formula for the sequence

  7. Arithmetic Sequence • EX 5: According to the National Education Association, teachers in the United States earned an average of $30,532 in 1990. This amount has increased by approximately $1472 per year. • A) Write a formula for the nth term of the arithmetic sequence that describes teachers’ average earnings n years after 1989 • B) How much will U.S. teachers earn, on average, by the year 2010?

  8. The Sum of the First n Terms of an Arithmetic Sequence • The sum of the first terms of an arithmetic sequence is given by: in which is the first term, is the common difference and is the nth term

  9. Sum of n terms • EX 6: Find the sum of the first 100 terms of the arithmetic sequence:

  10. EX 7: Find the Sum • A) • B)

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