If 7 and 189 are the first and fourth terms of geometric progression respectively, find the sum of the first three terms of the progression
-
A.
182 -
B.
91 -
C.
63 -
D.
28
Correct Answer: Option B
Explanation
(T_{n} = ar^{n – 1}) (nth term of a G.P)
(T_{4} = ar^{3} = 189)
(7 times r^{3} = 189 implies r^{3} = 27)
(r = sqrt[3]{27} = 3)
(S_{n} = frac{a(r^{n} – 1)}{r – 1})
(S_{3} = frac{7(3^{3} – 1)}{3 – 1} )
= (frac{7 times 26}{2} = 91)