If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first four for term
A
-45
B
-15
C
15
D
33
E
45
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
\(T_2\) = 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
Source: Myschool Past Questions Archive (Record #21978)