Chapter 1.1, Problem 45PPSE

Solution

a.

To explain: The pattern of the numbers $144,72,36,\mathrm{...}$ .

Given information:

The given pattern of numbers are $144,72,36,\mathrm{...}$

Explanation:

Here the first number is $144,$ and the second number is $72$, here second number is half of the first number similarly the third number is the half of the second number.

The rule of the pattern:

  $a_n=\frac{a_{n-1}}{2},\text{where}{a}_0=144$

Thus the pattern is following number is the half of the preceding number.

b.

To find: The first non integer from pattern of the numbers $144,72,36,\mathrm{...}$ .

The first non integer number in this pattern is $4.5$ .c

Given information:

The given pattern of numbers is $144,72,36,\mathrm{...}$

Concept used:

The rule of the pattern here is following number is the half of the preceding number.

Calculations:

The rule of the pattern is $a_n=\frac{a_{n-1}}{2},\text{where}{a}_0=144$ .

Find the first non-integer number, make the pattern according to rule.

  $144,72,36,18,9,\mathrm{4.5...}$

Thus, the first non-integer number is 4.5.