Question

Which term of the progression $18,-12,8,\dots$. 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 $r=-\frac{12}{18}=-\frac{2}{3}$
$T_n=\frac{512}{729}$
$T_n=a^{n-1}=18{\left(\frac{-2}{3}\right)}^{n-1}=\frac{512}{729}$
$\Rightarrow {\left(-\frac{2}{3}\right)}^{n-1}={\left(\frac{2}{3}\right)}^8$
$\therefore n-1=8,n=9$