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 is B

\(T_{n} = ar^{n - 1}\) (nth term of a G.P)

\(T_{4} = ar^{3} = 189\)

\(7 \times r^{3} = 189 \implies r^{3} = 27\)

\(r = \sqrt[3]{27} = 3\)

\(S_{n} = \frac{a(r^{n} - 1)}{r - 1}\)

\(S_{3} = \frac{7(3^{3} - 1)}{3 - 1} \)

= \(\frac{7 \times 26}{2} = 91\)