What is the sum of the first six terms of the series? 40−10+2.5−0.625+... What is the answer as a simplified fraction

Given Data:
Series: $40-10+2.5-0.625+...$
The first term of series is: a=40
The second term of series is: $a_2=-10$
The third term of series is: $a_3=2.5$
For the first and second term,
The common ratio of the series is,
$r=\frac{a_2}{a}$
Substitute the values in the above equation.
$r=\frac{-10}{40}$
$=-0.25$
For the second and third term
The common ratio of the series is,
$r=\frac{a_3}{a_2}$
Substitute the values in the above equation.
$r=\frac{2.5}{-10}$
$=-0.25$
So, the given series is a geometric series.
The sum of the first six terms of the geometric series is,
$S_6=a\frac{(1-r^6)}{(1-r)}$
Substitute the values in the above equation.
$S_6=(40)\frac{(1-(-0.25{)}^6)}{(1-(-0.25))}$
$=40\frac{(0.9998)}{1.25}$
$=31.99$
Thus, the sum of the first six terms of the given geometric series is 31.99.