Chapter 8.3, Problem 46SR

To determine

To calculate: To write an equation that describes the sequence $7,8,9,10,\mathrm{...}$ and then find the 14^thterm of the sequence.

Answer to Problem 46SR

Equation that describes the sequence is $t=n+6$ and the 14^th term of sequence is $20$

Explanation of Solution

Given information: Sequence is $7,8,9,10,\mathrm{...}$

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:

  $7,8,9,10,\mathrm{...}$

Here, $7$ is the term and its term number is $1$

Also, the common difference is

  $8-7=1$

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

Thus, the given sequence can be described in symbols as follows:

  $t=n+6$

Also, 14^th term of sequence is calculated as follows:

  $\begin{array}{l}{t}_{14}=14+6\\ t_{14}=20\end{array}$

Hence, the equation that describes the sequence is $t=n+6$ and the 14^th term of sequence is $20$