Chapter 1.2, Problem 49E

To determine

To describe the pattern observed in the table and complete the table with a variable expression $n$ .

Answer to Problem 49E

The complete table can be written as:

1	2	3	4	…	$n$
1	8	27	64	…	$n^3=n\cdot n\cdot n$

Explanation of Solution

Given information:

The table is given as:

1	2	3	4	…	$n$
1	8	27	64	…	?

Calculation:

From the table provided in the question, it can be observed that the numbers in first row follows the series of consecutive integers and second row follows the pattern in which the numbers in the first row raised to the third power.

So, for $nth$ integer, the number in the second column will be:

  $n^3=n\cdot n\cdot n$

Hence, the complete table can be written as:

1	2	3	4	…	$n$
1	8	27	64	…	$n^3=n\cdot n\cdot n$