The 6th term of a G.P is \(\frac{-2}{27}\) and its first term is 18. What is the common ratio?
A
-1/2
B
-1/3
C
1/4
D
2
E
3
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
a, ar, ar\(^2\), ar\(^3\), ar\(^4\), ar\(^5\)
6th term = ar\(^5\) = \(\frac{-2}{27}\)
1st term = a = 18
=> ar\(^5\)
= 18r\(^5\) =\(\frac{-2}{27}\)
r\(^5\) = \(\frac{-2}{27 * 18}\)
→ \(\frac{-1}{27 * 9}\)
r\(^5\) = \(\frac{-1}{243}\)
r = \(^5\)\sqrt[\(\frac{-1}{243}\)]
r = \(\frac{-1}{3}\)
Source: Myschool Past Questions Archive (Record #23791)