Chapter 14, Problem 5MPS

(a)

To determine

To Find: The distance travelled in the 8^th minute.

Answer to Problem 5MPS

The distance travelled in the eight minute is $\frac{1}{64}\text{cm}$ .

Explanation of Solution

Given:

The snail moves 2 cm in one minute.

Calculation:

Consider the formula for the nth term of the geometric sequence is,

  $t_n=t_1\cdot r^{n-1}$

The first term is two as the snail moves 2 cm in one minute and in the succeeding minutes the snail travels half as far as the previous one. Then, the general ratio of the GP is.

  $r=\frac{1}{2}$

Then, the in the eight minute the distance travelled by the snail is,

  $\begin{array}{c}{t}_n=2\cdot {\left(\frac{1}{2}\right)}^{8-1}\\ =2\cdot {\left(\frac{1}{2}\right)}^7\\ =\frac{1}{64}\text{cm}\end{array}$

(b)

To determine

To Find: The distance travelled if the snail travels for forever.

Answer to Problem 5MPS

The distance travelled in the infinite time is $4\text{cm}$ .

Explanation of Solution

Given:

The snail moves 2 cm in one minute.

Calculation:

Consider the formula for the sum of infinite geometric sequence is,

  $S=\frac{t_1}{1-r}$

Then, the distance travelled in infinite time is,

  $\begin{array}{c}S=\frac{2}{1-\frac{1}{2}}\\ =4\text{cm}\end{array}$