If the second and fifth terms of a GP are 24 and 3 respectively, then the sum of first six terms is

Options

A. 181
B. `(181)/(2)`
C. `189`
D. `(189)/(2)`

Answer

D

Explanation

Let first term and common ratio of a GP be a and r, respectively.
Given, `T_(2)=24 and T_(5)=3`
`thereforear=24 and ar^(4)=3`
Now, `(ar^(4))/(ar)=(3)/(24)`
`impliesr^(3)=(1)/(8)`
`impliesr=(1)/(2)`
`thereforea((1)/(2))=24 impliesa=48`
Now, `S_(n)=(a|a-(r)^(6)])/(1-r)=(48[1-((1)/(2))^(6)])/(1-(1)/(2))`
`=(48(1-(1)/(64)))/((1)/(2))=(48*(63)/(64))/((1)/(2))=(189)/(2)`