If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term

A.

-45

B.

-15

C.

15

D.

33

E.

45

Correct answer is E

T\(_{2}\) = ar = 6

T\(_{5}\) = ar\(^{4}\) = 48

\(\frac{T_5}{T_2}\) = \(\frac{ar^{4}}{ar}\) = \(\frac{48}{6}\)

= r\(^{3}\) = 8

⇒ r = 2

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

S\(_{4}\) = \(\frac{a((r^4) - 1)}{r - 1}\)

S\(_{4}\) = \(\frac{3((2^4) - 1)}{2 - 1}\)

= 3(16 -1)

= 45