For an arithmetic series
a, a+d, a+2d, a+3d, ...
where a is the first term and d is the common difference, the sum of n terms equals
[tex]S_n=na+\frac{n(n-1)}{2}d[/tex]
Since the first step requires 1.6 cubic feet of concrete, a = 1.6.
Now, the first 5 steps require 24 cubic feet of concrete, that is,
[tex]S_5=24[/tex]
So,
[tex]\begin{gathered} 5(1.6)+\frac{5\cdot4}{2}d=24 \\ 8+10d=24 \\ 10d=16 \\ d=1.6 \end{gathered}[/tex]
Find the concrete required for 10 steps.
[tex]\begin{gathered} S_{10}=10(1.6)+\frac{10\cdot9}{2}(1.6) \\ =16+45(1.6) \\ =88 \end{gathered}[/tex]
So, 88 cubic feet of concrete required for thr first 10 steps.
The second option is correct.
