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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

A construction worker is pouring concrete stairs The first step requires 16 cubic feet of concrete and the first 5 steps require a total of 24 cubic feet If the class=

Respuesta :

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.

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