Question
The 5th term of an arithmetic progression is 23 and the
12th term is 72. Find the first term and the common difference.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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