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UNKNOWN VALUES in ARITHMETIC SEQUENCES PRE228 ARITHMETIC SEQUENCE: a sequence of numbers where the same term is added (or subtracted) from one term to the next. For example: –3, –1, 1,_3_, 5, 7, 9, … 1. Find the common difference. Find the unknown number in the arithmetic sequence: 7 – 5 = 2 and 9 – 7 = 2 CD = +2 2. Apply the common difference to the missing term. 1 + 2 = 3
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UNKNOWN VALUES in ARITHMETIC SEQUENCES PRE228 How do you find the 21 st term in a sequence? a 1 : first term in the sequence n: number of term you want to find (27 th, 12 th, etc.) d: common difference a n = a 1 + (n – 1)d Given sequence: (–3, –1, 1, 3, 5, 7, 9, …) Find the 21 st term.
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UNKNOWN VALUES in ARITHMETIC SEQUENCES PRE228 How do you find the 21 st term in a sequence? a 1 : first term in the sequence n: number of term you want to find (27 th, 12 th, etc.) d: common difference a n = a 1 + (n – 1)d Given sequence: (–3, –1, 1, 3, 5, 7, 9, …) a 21 = –3 + (21 – 1)2 a 21 = –3 + (20)2 a 21 = –3 + 40 a 21 = 37
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UNKNOWN VALUES in ARITHMETIC SEQUENCES PRE228 Find a 7 (the 7 th term) in a sequence where the first term is 12 and the common difference is –4. a 7 = 12 + (7 – 1)–4 a 7 = 12 + (6)–4 a 7 = 12 + –24 a 7 = –12 a n = a 1 + (n – 1)d
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