Chapter 11.5, Problem 8P

To determine

To find: the number of amount to be pay if the payment exceeds three week instead of two.

Answer to Problem 8P

Plan $A$

  $\$231$ and Plan $B$

  $\$20971.51$ .

Explanation of Solution

Given:

Three weeks contain $21$ days.

Sum of $21$ days is considered.

Concept used:

Generic geometric sequence:

  $a_1,a_2,a_3\mathrm{.....}{a}_{n-1}.$

There is common ratio:

  $c.r=\frac{a_n}{a_{n-1}}$ .

The geometric progression:

  $a,ar,a{r}^2\mathrm{.....}a{r}^{n-1}.$

Last term or nth term of the geometric progression will be:

  $t_n=a{r}^{n-1}$ .

  $s_n=\frac{a\left(1-r^n\right)}{1-r};s_{\infty }=\frac{a_1}{1-r}$ .

Calculation:

Using the formulas for summing arithmetic and geometric series.

Plan A: arithmetic series with sum of:

  $\frac{21\left(1+21\right)}{2}=231.$

Plan $B$ : geometric series with sum of:

  $\frac{0.01\left(1-2^{21}\right)}{1-2}=0.01\times 2097151=20,971.51$ .

Hence, plan $A$

  $\$231$ , plan $B$

  $\$20971.51$ .