Chapter SH, Problem 8.2.11EP

To determine

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

Answer to Problem 8.2.11EP

Sequence is described by equation $t_n=7n-1$ and $t_{38}=265$

Explanation of Solution

Given information:Sequence is $6,13,20,\mathrm{.....}$ and term is $38th$

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:

  $6,13,20,\mathrm{.....}$

Here,

  $a=6$

  $d=13-6=20-13=7$

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

  $\begin{array}{l}{t}_n=6+\left(n-1\right)\left(7\right)\\ t_n=6+7n-7\\ t_n=7n-1\end{array}$

Also,38^thterm of sequence is calculated as

  $\begin{array}{l}{t}_{38}=7\left(38\right)-1\\ t_{38}=266-1\\ t_{38}=265\end{array}$

Conclusion:

Hence, Sequence is described by equation $t_n=7n-1$ and $t_{38}=265$