From $5^\text{th}$ To $1^\text{st}$

Given: common ratio $r = 4$

Sum of first $5$ terms is $S_n=1023$

Formula for finding sum of finite terms in Geometric Progression $S_n=a \cdot \dfrac{(1 - r^n)}{1-r}$

Placing the value in the above formula,

$1023=a \cdot \dfrac{(1-1024)}{1-4} \\ a =\dfrac{-3069}{-1023} \\ \boxed{a = 3}$

We write the sum of the terms as $a+4a+16a+64a+256a=1023$ , since the common ratio is $4$ .

Factor out $a$ and sum: $a(1+4+16+64+256)=a(341)=1023$ .

Dividing, we find $a=3$ .

For sum of 5 terms = 1023, a can not be 1 as it would result in 5, cant be 2, 4 coz the result would have been an even no. then. So the answer is 3.