Chapter 11.5, Problem 4P

To determine

To calculate:

The number of strikes occurs in one day by clock’s bell

Answer to Problem 4P

  $216$ times the clock’s bell strikes in one day

Explanation of Solution

Given information:

  $t=4hrs.$

Calculation:

First need to calculate the series for the first $t=4hrs.$ Now, to get the values for the entire day $\left(t=4hrs.\right)$ , multiply by $6$ .

Hence, the clock series starts from one bell and ends on eighth bell. Therefore consider,

  $\begin{array}{l}{t}_1=1\\ t_8=8\end{array}$

Sum value for the first four hours is $S_{15}$ . Need to find out the sum value $S_{15}$ :

  $\begin{array}{l}{S}_8=\frac{n\left(t_1+t_8\right)}{2}\\ S_8=\frac{8\left(1+8\right)}{2}\\ S_8=36\end{array}$

Multiply by $6$ :

  $S_{24}=S_8\times 6=36\times 6=216$

Therefore, the number of strikes occurs in one day by clock’s bell is $216$