The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms

A.
60 
B.
62 
C.
54 
D.
64
Correct Answer: Option B
Explanation
T_{2} = 4, T_{4} = 16
T_{x} = ar^{n1}
T_{2} = ar^{21} = 4 i.e. ar^{3} = 16, i.e. ar = 4
T_{4} = ar^{41}
therefore, (frac{T_4}{T_r}) = (frac{ar^3}{ar}) = (frac{16}{4})
r^{2} = 4 and r = 2
but ar = 4
a = (frac{4}{r}) = (frac{4}{2})
a = 2
S^{n} = (frac{a(r^n – 1)}{r – 1})
S^{5} = (frac{2(2^5 – 1)}{2 – 1})
= (frac{2(32 – 1)}{2 – 1})
= 2(31)
= 62