Chapter 7.1, Problem 23E

Solution

To state: The pattern, the next term for the sequence $3.1,3.8,4.5,5.2,\dots$ .

The resultant term is $5.9$ and rule is $a_n=0.7n+2.4$ .

Given information:

The given sequence is $3.1,3.8,4.5,5.2,\dots$ .

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,

  $3.1,3.8,4.5,5.2,\dots$

It can be seen from the given sequence that the common difference of each term is 0.7. Then the first term can be written as: $0.7\left(1\right)+2.4=3.1$

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

  $0.7\left(1\right)+2.4,0.7\left(2\right)+2.4,0.7\left(3\right)+2.4,0.7\left(4\right)+2.4,\dots$

The next terms is:

  $\begin{array}{c}0.7\left(5\right)+2.4=3.5+2.4\\ =5.9\end{array}$

A rule for the nth term is $a_n=0.7n+2.4$ .

Therefore, the next term of the given sequence is $5.9$ and the rule it represents is $a_n=0.7n+2.4$ .