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Answer :

Given,

Distance between the rungs of the ladder is 25 cm.

Distance between the top rung and bottom rung of the ladder is =

\({2} {\dfrac{1}{2}}m \)

\( = {2} {\dfrac{1}{2}} (100)cm \)

\( = {{5} \over {2}} ×100\) cm

= 250 cm

Therefore, total number of rungs = \({{250} \over {25}} + 1 = 11\)

As we can see from the figure, the ladder has rungs in decreasing order from top to bottom. Thus, we can conclude now, that the rungs are decreasing in an order of AP.

And the length of the wood required for the rungs will be equal to the sum of the terms of AP series formed.

So,

First term, a = 45

Last term, l = 25

Number of terms, n = 11

Now, as we know, sum of nth terms is equal to,

\(S_n= {{n} \over {2}}(a+ l)\)

\(S_n= {{11} \over {2}}(45+25) \)

\( = {{11} \over {2}}(70) = 385\) cm

Hence, the length of the wood required for the rungs is 385 cm.

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- The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x. [Hint :Sx – 1 = S49 – Sx]
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