Question

Question 3 A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are m apart, what is the length of the wood required for the rungs? [Hint: number of rungs]

Class 10 - Math - Arithmetic Progressions Page 115

Answer 1

Sum of n terms of an AP

The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by

Sn = n /2 [ 2a + ( n - 1) d] or

Sn=n /2 [ a + l ]       (l = last term)

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

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Hope this will help you........

Answer 2

HI !

Distance between first and last rung = 2.5 m = 250 cm

Distance between first and second rung = 25 cm


No: of rungs = 250/25 +1 = 11 rungs
a = 45 , n = 11 , l = 25

Length of wood required = Sn = n/2 (a + l )
= 11/2 (45+25 )
= 11/2 (70)
= 385 cm