Theory question 104
Sequences and SeriesThe sum of the first twelve terms of an Arithmetic Progression (A.P) is 168. If the third term is 7, find the values of the common difference and the first term.
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Model answer
S₁₂ = 6(2a + 11d) = 168, so 2a + 11d = 28.
a + 2d = 7, so 2a + 4d = 14.
Subtracting: 7d = 14, d = 2; a = 3.
Explanation
Set up two equations in a and d.