Chapter SH, Problem 8.2.14EP

To determine

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

Answer to Problem 8.2.14EP

Sequence is described by equation $t_n=5+0.5n$ and $t_{30}=20$

Explanation of Solution

Given information:Sequence is $5.5,6,6.5,\mathrm{....}$ and term is $30th$

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:

  $5.5,6,6.5,\mathrm{....}$

Here,

  $a=5.5$

  $d=6-5.5=6.5-6=0.5$

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

  $\begin{array}{l}{t}_n=5.5+\left(n-1\right)\left(0.5\right)\\ t_n=5.5+0.5n-0.5\\ t_n=5+0.5n\end{array}$

Also,30^thterm of sequence is calculated as

  $\begin{array}{l}{t}_{30}=5+0.5\left(30\right)\\ t_{30}=5+15\\ t_{30}=20\end{array}$

Conclusion:

Hence, Sequence is described by equation $t_n=5+0.5n$ and $t_{30}=20$