2.the second term of an arithmetic sequence is 24 and the fifth term is 3.find the first term and the common differnce ANSWER : The common difference is -7 and the first term is 31. STEP BY STEP EXPLANATION : Find the common difference by linear sistem. A1 + 4R = 3 (-1) A1 + 1R = 24 _______________ -A1 - 4R = -3 A1 + 1R = 24 _______________ -3R = 21 R = 21/(-3) R = -7 The first term. An = A1 + (n - 1) × d 3 = A1 + (5 - 1) × (-7) 3 = A1 + 4 × (-7) 3 = A1 + (-28) A1 - 28 = 3 A1 = 3 + 28 A1 = 31 Therefore , the common difference is -7 and the first term is 31. OK.
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