Chapter 8.3, Problem 47SR

To determine

To calculate: To write an equation that describes the sequence $6,10,14,18,\mathrm{....}$ and then find the 23^rdterm of the sequence.

Answer to Problem 47SR

Equation that describes the sequence is $t=2+4n$ and the 23^rdterm of sequence is $94$

Explanation of Solution

Given information: Sequence is $6,10,14,18,\mathrm{....}$

Formula Used:

Term: In a sequence, each number is referred to as a term

Term Number: In a sequence, the position of the given term is referred to as term number.

When the difference between the consecutive terms of a sequence is common, then the sequence is an arithmetic sequence.

Calculation:

Sequence is given as follow:

  $6,10,14,18,\mathrm{....}$

Here, the first term of the sequence is $a=6$

Also, the common difference is

  $d=10-6=14-10=4$

Since the difference is common, hence the sequence in arithmetic sequence.

Let term is denoted by $t$ and term number is denoted as $n$

Thus, nth term of arithmetic sequence is given as

  $t=a+\left(n-1\right)d$

Substituting the values in above equation,

  $\begin{array}{l}t=6+\left(n-1\right)4\\ t=6+4n-4\\ t=2+4n\end{array}$

Also, 23^rdterm of sequence is calculated as follows:

  $\begin{array}{l}{t}_{23}=2+4\left(23\right)\\ t_{23}=2+92\\ t_{23}=94\end{array}$

Hence, the equation that describes the sequence is $t=2+4n$ and the 23^rdterm of sequence is $94$