Class 10

Math

All topics

Arithmetic Progressions

A ladder has rungs $25$ cm apart. The rungs decrease uniformly in length from $45$ cm at the bottom to $25$ cm at the top. If the top and the bottom rungs are $221 m$ apart, what is the length of the wood required for the rungs

It is given that the rungs are $25$ cm apart and the top and bottom rungs are $221 $ m apart.

$∴$ the total number of rungs.

$25221 ×100 +1$

$=$ $25250 +1=11$

Now, as the lengths of the rungs decrease uniformly, they will be in an A.P.

The length of the wood required for the rungs equals the sum of all the terms of this A.P.

First term, $a=45$

Last term, $l=25$

$n=11$

$S_{n}=2n (a+l)$

$S_{10}=211 (45+25)=211 ×70=385$ cm

Therefore, the length of wood is $385$cm