A ladder

The ladder's bottom rung is 36 inches long, and the topmost rung is 24 inches long. If the ladder has 18 rungs, how many inches each other rung is shorter than the rung below it? How many feet of wood were used to make the rungs?

Correct answer:

d =  0.7059 inch
t =  45 ft

Step-by-step explanation:

$$\begin{gathered} n=18 \\ {a}_1=24\text{inch} \\ {a}_{18}=36\text{inch} \\ {a}_{18}=a_1+(n-1)\cdot d \\ d=\frac{a_{18}-a_1}{n-1}=\frac{36-24}{18-1}=\frac{12}{17}\text{inch}=0.7059\text{inch} \end{gathered}$$

$$\begin{gathered} s=n\cdot \frac{a_1+a_{18}}{2}=18\cdot \frac{24+36}{2}=540\text{inch} \\ t=s\to \text{ft}=s:12\text{ft}=540:12\text{ft}=45\text{ft}=45\text{ft} \end{gathered}$$

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