Question

4. A ladder has 50 rungs. The bottom rung is 1 m long. Each rung is 12,5 mm shorter than the rung beneath it. Determine the total length of wood required to make 50 rungs.​

Answer 1

Using an arithmetic sequence, it is found that the total length of wood required to make 50 rungs is of 34.6875 m.

What is an arithmetic sequence?

• In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

$a_n = a_1 + (n-1)d$

The sum of the first n terms is given by:

$S_n = \frac{n(a_1 + a_n)}{2}$

In this problem:

• A ladder has 50 rungs, hence the sequence has 50 terms, that is, $n = 50$.

• The bottom rung is 1 m long, hence, considering it as the first term, $a_1 = 1$.

• Each rung is 12,5 mm shorter than the rung beneath it, hence, in meters, the common difference is of $d = -0.0125$.

Then the 50th term is:

$a_50 = a_1 + (n-1)d = 1 - 0.0125(49) = 0.3875$

The total length is the sum of the first 50 terms, hence:

$S_{50} = \frac{50(1 + 0.3875)}{2} = 25(1.3875) = 34.6875$

The total length of wood required to make 50 rungs is of 34.6875 m.

You can learn more about arithmetic sequence at brainly.com/question/6561461