Question

The seventh term of a G.P. is 27 times the fourth term and the fifth term is 243. The third term of this G.P. is .

• A. 9
• B. 81
• C. 27
• D. 36

Answer 1

The correct option is C 27

Let $a$ be the first term and $r$ be the common ratio of the G.P.
Given, $a_7=27a_4.$
$\Rightarrow a{r}^6=27a{r}^3$
$\Rightarrow r^3=27$
$\Rightarrow r=3$
Given that $a_5=243.$
$\Rightarrow a{r}^4=243$
i.e., $a(3{)}^4=243$
$\Rightarrow a=3$
Now, $a_3=a{r}^2=3(3{)}^2=27.$