Chapter SH, Problem 8.2.8EP

To determine

To calculate: To describe the equation that describes the sequence and then find the indicated term

Answer to Problem 8.2.8EP

Sequence is described by equation

  $t_n=19-n$ and $t_{13}=6$

Explanation of Solution

Given information:Sequence is $18,17,16,\mathrm{...}$ and term is $13th$

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:

  $18,17,16,\mathrm{...}$

Here,

  $a=18$

  $a=17-18=16-17=-1$

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

  $\begin{array}{l}{t}_n=18+\left(n-1\right)\left(-1\right)\\ t_n=18-n+1\\ t_n=19-n\end{array}$

Also,13^thterm of sequence is calculated as

  $\begin{array}{l}{t}_{13}=19-13\\ t_{13}=6\end{array}$

Conclusion:

Hence, Sequence is described by equation $t_n=19-n$ and $t_{13}=6$