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: Option 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)