Respuesta :
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:
[tex]a_n = a_1 + (n-1)d[/tex]
The sum of the first n terms is given by:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In this problem:
- A ladder has 50 rungs, hence the sequence has 50 terms, that is, [tex]n = 50[/tex].
- The bottom rung is 1 m long, hence, considering it as the first term, [tex]a_1 = 1[/tex].
- Each rung is 12,5 mm shorter than the rung beneath it, hence, in meters, the common difference is of [tex]d = -0.0125[/tex].
Then the 50th term is:
[tex]a_50 = a_1 + (n-1)d = 1 - 0.0125(49) = 0.3875[/tex]
The total length is the sum of the first 50 terms, hence:
[tex]S_{50} = \frac{50(1 + 0.3875)}{2} = 25(1.3875) = 34.6875[/tex]
The total length of wood required to make 50 rungs is of 34.6875 m.
You can learn more about arithmetic sequence at https://brainly.com/question/6561461
