Question

A construction worker is pouring concrete stairs. The first step requires 1.6 cubic feet of concrete, and the first 5 steps require a total of 24 cubic feet. If the steps follow an arithmetic series, how much concrete is required for the first 10 steps?48 cubic feet88 cubic feet106 cubic feet160 cubic feet

Answer 1

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

`S_n=na+(n(n-1))/(2)d`

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,

`S_5=24`

So,

`\begin{gathered} 5(1.6)+(5\cdot4)/(2)d=24 \\ 8+10d=24 \\ 10d=16 \\ d=1.6 \end{gathered}`

Find the concrete required for 10 steps.

`\begin{gathered} S_(10)=10(1.6)+(10\cdot9)/(2)(1.6) \\ =16+45(1.6) \\ =88 \end{gathered}`

So, 88 cubic feet of concrete required for thr first 10 steps.

The second option is correct.