Question

Which term of the progression $18,-12,8, \ldots$. is $\frac{512}{729} ?$

• A. $9^{\text {th }}$
• B. $10^{\text {th }}$
• C. $8^{\text {th }}$
• D. $7^{\text {th }}$

Answer 1

Answer: (A)

Here first term of G.P. $a =18$
and common ratio $r=-\frac{12}{18}=-\frac{2}{3}$
$ T_n=\frac{512}{729} $
$ T_n=a^{n-1}=18\left(\frac{-2}{3}\right)^{n-1}=\frac{512}{729} $
$ \Rightarrow \left(-\frac{2}{3}\right)^{n-1}=\left(\frac{2}{3}\right)^8 $
$ \therefore n-1=8, n=9$