# Arithmetic Sequences Finding the nth Term. Arithmetic Sequences A pattern where all numbers are related by the same common difference. The common difference.

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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. 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.

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. a n = a 1 + (n – 1)(d) a n = the answer term you are looking for in the sequence a 1 = 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 63 rd term a n = 23 + (63 – 1)(-5) a n = 23 + 62(-5) a n = 23 + (-310) = -287

Practice Problems 1.11, 13, 15, 17, …Find the 85 th term 2.25, 22, 19, 16, …Find the 50 th term 3.a 1 = -15 d = +4 Find the 71 st term 4.a n = 255 d = +3 a 1 = 36 Find n

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