Respuesta :
Using an arithmetic sequence, it is found that the clock chimes 132 times in a 24-h period.
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]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In this problem, as the day is divided in two 12-hours period, the total will be twice the sum of the 12 elements of the following sequence:
{0, 1, 2, 3, ..., 11}
In which [tex]a_1 = 0, a_11 = 11, n = 12[/tex].
Then:
[tex]T = 2\frac{12(0 + 11)}{2} = 12 \times 11 = 132[/tex]
The clock chimes 132 times in a 24-h period.
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
