Chapter 7.1, Problem 26E

Solution

To state: The pattern, the next term for the sequence $9,16.8,24.6,32.4,\dots$ .

The resultant term is $40.2$ and rule is $a_n=7.8n+1.2$ .

Given information:

The given sequence is $9,16.8,24.6,32.4,\dots$ .

Explanation:

A sequence is a function whose domain is a set of consecutive integers. If a domain is not specified, it is understood that domain starts with 1.

Now consider the given sequence,

  $9,16.8,24.6,32.4,\dots$

It can be seen from the given sequence that the common difference of each term is $7.8$ . Then the first term can be written as: $7.8\left(1\right)+1.2=9$

Similarly, the given terms of the sequence can be written as:

  $7.8\left(1\right)+1.2,7.8\left(2\right)+1.2,7.8\left(3\right)+1.2,7.8\left(4\right)+1.2,\dots$

The next terms is:

  $\begin{array}{c}7.8\left(5\right)+1.2=39.0+1.2\\ =40.2\end{array}$

A rule for the nth term is $a_n=7.8n+1.2$ .

Therefore, the next term of the given sequence is $40.2$ and the rule it represents is $a_n=7.8n+1.2$ .