Answer
a) 8 steps
b) 1100 bricks
Work Step by Step
Consider the arithmetic sequence:
$n=25$
$a_1=80$
$d=-3$
a) Determine $a_{25}$ (the number of bricks for the top step):
$a_n=a_1+(n-1)d$
$a_{25}=80+(25-1)(-3)=80+24(-3)=80-72=8$
So there are 8 bricks in the top step.
b) Determine $S_{25}$, the sum of the bricks for the 25 steps:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$S_{25}=\dfrac{25(a_1+a_{25})}{2}=\dfrac{25(8+80)}{2}=1100$
