Question

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 21 2 m apart, what is the length of the wood required for the rungs?

Answer 1

Distance between the starting rung and the top most rung = 250 cm

Number of rungs in 250 cm with spacing of 25 cm = 250/25 = 10

Including the bottom most rung the total number of rungs on the ladder = 11

The length of rungs is an Arithmetic progression/series.

Sum of lengths of all 11 rungs = (1st term + last term)/2  * number of rungs
                   = (45+25)/2 * 11 = 385 cm