Chapter SH, Problem 8.2.6EP

To determine

To calculate: To describe the sequence using words and symbols

Answer to Problem 8.2.6EP

Sequence is described by equation $t_n=1+3n$

Explanation of Solution

Given information:Sequence is $4,7,10,\mathrm{.....}$

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.

Nth term of arithmetic series is given as

  $t_n=a+\left(n-1\right)d$

Where,

  $t_n=$ nth term

  $a=$ first number

  $d=$ common difference

Calculation:

Sequence is given as follow:

  $4,7,10,\mathrm{.....}$

Here,

  $a=4$

  $d=7-4=10-7=3$

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

  $\begin{array}{l}{t}_n=4+\left(n-1\right)3\\ t_n=4+3n-3\\ t_n=1+3n\end{array}$

In words, term is one more than three times the term number

Conclusion:

Hence, Sequence is described by equation $t_n=1+3n$