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

Correct answer is B

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 = \(^5\)√[\(\frac{-1}{243}\)]

 

r = \(\frac{-1}{3}\)