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Arithmetic Sequences Finding the nth Term

Arithmetic Sequences Finding the nth Term. Arithmetic Sequences . A pattern where all numbers are related by the same common difference. The common difference must be an addition or subtraction constant. The common difference can be used to predict future numbers in the pattern.

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Arithmetic Sequences Finding the nth Term

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  1. Arithmetic SequencesFinding the nth Term

  2. Arithmetic Sequences • A pattern where all numbers are related by the same common difference. • The common difference must be an addition or subtraction constant. • The common difference can be used to predict future numbers in the pattern. • Ex. 4, 7, 10, 13, ___, ___, ___ The common difference in this pattern is +3. Based on this information, you can say that the next 3 terms will be 16, 19, and 22. Ex. -1, -5, -9, ___, ___, ___ The common difference in this pattern is -4. Based on this information, you can say that the next 3 terms will be -13, -17, and -21.

  3. Finding the nth Term • If you want to find a term in an arithmetic sequence that is far into the pattern, there is a formula to use. an = a1 + (n – 1)(d) an = the answer term you are looking for in the sequence a1 = the first term in the sequence n = the ordinal number term you are looking for in the sequence d = the common difference Ex. 23, 18, 13, 8, … find the 63rd term an = 23 + (63 – 1)(-5) an = 23 + 62(-5) an = 23 + (-310) = -287

  4. Practice Problems • 11, 13, 15, 17, … Find the 85th term • 25, 22, 19, 16, … Find the 50th term • a1 = -15 d = +4 Find the 71st term • an = 255 d = +3 a1 = 36 Find n

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