Chapter 1.2, Problem 37E

a.

To determine

To calculate: The missing values the table and identify any pattern that is seen

Answer to Problem 37E

The table can be written as follows:

  

Explanation of Solution

Given:

The following table:

  

Calculation:

For column 3, the missing value will be the sum of $\text{1,3}$ and $\text{5}$ which is $\text{9}$ .

For column 4, the missing value will be the sum of $\text{1,3,5}$ and $\text{7}$ which is $\text{16}$ .

For column 5, the missing value will be the sum of $\text{1,3,5,7}$ and $\text{9}$ which is $\text{25}$ .

A pattern observed here is that the sum is always equal to the square of the number of terms.

b.

To determine

To write: The variable expression for the sum of $n$ odd numbers.

Answer to Problem 37E

The variable expression for the sum of $n$ odd numbers is $n^2$

Explanation of Solution

Given:

The following table:

  

To find the sum of first $n$ odd numbers, $n$ being the number of terms, find the square of $n$ .

For example, to find sum of first $10$ odd numbers, find ${10}^2$ .

c.

To determine

To calculate: sum of first $100$ odd numbers.

Answer to Problem 37E

Sum of first $100$ odd numbers is $10000$

Explanation of Solution

Given:

First $100$ odd numbers.

Calculation:

Here, $n$ is $100$ . To find the sum of first $100$ odd numbers, $n$ is squared. Therefore,

  $n^2={100}^2=10000$