Chapter SH, Problem 8.2.7EP

To determine

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

Answer to Problem 8.2.7EP

Sequence is described by equation $t_n=5n$ and $t_{23}=105$

Explanation of Solution

Given information:Sequence is $5,10,15,\mathrm{.....}$ and term is $23rd$

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:

  $5,10,15,\mathrm{.....}$

Here,

  $a=5$

  $d=10-5=15-10=5$

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

  $\begin{array}{l}{t}_n=5+\left(n-1\right)5\\ t_n=5+5n-5\\ t_n=5n\end{array}$

Also, 23^rd term of sequence is calculated as

  $\begin{array}{l}{t}_{23}=5\left(23\right)\\ t_{23}=105\end{array}$

Conclusion:

Hence, Sequence is described by equation $t_n=5n$ and $t_{23}=105$