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    Question

    The 5th term of an arithmetic progression is 23 and the

    12th term is 72. Find the first term and the common difference.
    A -5 and 7 Correct Answer Incorrect Answer
    B 5 and -2 Correct Answer Incorrect Answer
    C 2 and 5 Correct Answer Incorrect Answer
    D -2 and -8 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let first term = a Common difference = d T₅ = a + 4d = 23 T₁₂ = a + 11d = 72 Subtract the two equations: (a + 11d) – (a + 4d) = 72 – 23 7d = 49 d = 7 Substitute back: a + 4×7 = 23 a + 28 = 23 a = –5 Answer: First term = –5 Common difference = 7

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