The 4th term of a G.P is 3 and its first term is 81. What is its common ratio?
A
3
B
\(\frac{2}{3}\)
C
\(\frac{1}{3}\)
D
-\(\frac{1}{3}\)
E
-3
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
T\(_4\) = 3 = ar\(^3\)
a = 81
3 = 81 r\(^3\)
divide through by 81
r\(^3\) = \(\frac{1}{27}\)
take cube root of both sides
r = \(\sqrt[3]{\frac{1}{27}}\) = \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #42328)