A ladder

The bottom rung of a ladder 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 was used in making the rungs?

Correct result:

d =  0.7059 inch
t =  45 ft

Solution:

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

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

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