Question

If the second and fifth term of a G.P. is $3$ and $81$ respectively, then the first term of this G.P. is

• A. $9$
• B. $2$
• C. $1$
• D. $3$

Answer 1

The correct option is C $1$

Let $a$ be the 1st term and $r$ be the common ratio of the given G.P.
$a_2=3\Rightarrow ar=\mathrm{3.........}\left(i\right)$
$a_5=81\Rightarrow a{r}^4=\mathrm{81.....}\left(ii\right)$
Dividing equation (i) and (ii),
$r^3=27\Rightarrow r=3\Rightarrow a=1$