Chapter: Arithmetic Progression· Mathematics Part 1 (Algebra)
Answer: 4 terms or 13 terms
\(a = 24\), \(d = -3\), \(S_n = 78\)
\(78 = \dfrac{n}{2}[48 + (n - 1)(-3)] = \dfrac{n}{2}(51 - 3n)\)
\(156 = 51n - 3n^2 \Rightarrow 3n^2 - 51n + 156 = 0 \Rightarrow n^2 - 17n + 52 = 0\)
\((n - 4)(n - 13) = 0 \Rightarrow n = 4\) or \(n = 13\)
Both are valid. The 5th to 13th terms are 12, 9, 6, 3, 0, −3, −6, −9, −12, whose sum is 0, so adding them does not change the sum. Hence \(S_4 = S_{13} = 78\).