The sum of the first three terms of an Arithmetic Progression (A.P) is 18. If the first term is 4, find their product.
A. 130
B. 192
C. 210
D. 260
Correct Answer: B
Explanation
\(S_{n} = \frac{n}{2}(2a + (n - 1)d)\) ( for an arithmetic progression)
\(S_{3} = 18 = \frac{3}{2}(2(4) + (3 - 1) d) \)
\(18 = \frac{3}{2} (8 + 2d)\)
\(18 = 12 + 3d \implies 3d = 6\)
\(d = 2\)
\(\therefore T_{1} = 4 \implies T_{2} = 4 + 2 = 6; T_{3} = 6 + 2 = 8\)
Their product = \(4 \times 6 \times 8 = 192\)
