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PRE228 UNKNOWN VALUES in ARITHMETIC SEQUENCES ARITHMETIC SEQUENCE: a sequence of numbers where the same term is added (or subtracted) from one term to the next. Find the unknown number in the arithmetic sequence: For example: –3, –1, 1,_3_, 5, 7, 9, … 7 – 5 = 2 and 9 – 7 = 2 CD = +2 1. Find the common difference. 1+2=3 2. Apply the common difference to the missing term. PRE228 UNKNOWN VALUES in ARITHMETIC SEQUENCES How do you find the 21st term in a sequence? an = a1 + (n – 1)d a1: first term in the sequence n: number of term you want to find (27th, 12th, etc.) d: common difference Find the 21st term. Given sequence: (–3, –1, 1, 3, 5, 7, 9, …) PRE228 UNKNOWN VALUES in ARITHMETIC SEQUENCES How do you find the 21st term in a sequence? an = a1 + (n – 1)d a1: first term in the sequence n: number of term you want to find (27th, 12th, etc.) d: common difference Given sequence: (–3, –1, 1, 3, 5, 7, 9, …) a21 = –3 + (21 – 1)2 a21 = –3 + (20)2 a21 = –3 + 40 a21 = 37 PRE228 UNKNOWN VALUES in ARITHMETIC SEQUENCES an = a1 + (n – 1)d Find a7 (the 7th term) in a sequence where the first term is 12 and the common difference is –4. a7 = 12 + (7 – 1)–4 a7 = 12 + (6)–4 a7 = 12 + –24 a7 = –12