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Question: In an arithmetic sequence, t5 = 8 and t31 = - 44. Find "a" and "d"
In an arithmetic sequence, the nth term can be represented by the formula: tn = a + (n - 1)d, where tn is the nth term, a is the first term and d is the common difference. We have two equations from the given. t5 = a + 4d = 8 ...(Equation 1) t31 = a + 30d = -44 ...(Equation 2) To find 'a' and 'd', you can subtract Equation 1 from Equation 2 to get rid of 'a'. This will leave you with: a + 30d - (a + 4d) = -44 - 8 26d = -52 Solving for d, we find d = -52/26 = -2. Then, substitute d = -2 in Equation 1: a + 4(-2) = 8 a - 8 = 8 a = 8 + 8 = 16 So, a = 16 and d = -2.
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