Answer
The total number of weevils killed during the first five days is 8525.
Work Step by Step
The situation can be modeled by a geometric sequence, with $a_{1} = 6400$ and $r = \frac{1}{4}$, which the general term $a_{n} = 6400(\frac{1}{4})^{n-1}$, where n is the number of days taken.
For the total number of weevils killed during the first five days, it will be equal to $\sum\limits_{n=1}^5 a_{n} = \sum\limits_{n=1}^5 6400(\frac{1}{4})^{n-1}$
= $\frac{6400(1 - (\frac{1}{4})^5)}{(1 - \frac{1}{4})}$
= 8525 weevils killed