Chapter SH, Problem 8.2.12EP

To determine

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

Answer to Problem 8.2.12EP

Sequence is described by equation $t_n=2n-6$ and $t_{67}=128$

Explanation of Solution

Given information:Sequence is $-6,-4,-2,\mathrm{....}$ and term is $67th$

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:

  $-6,-4,-2,\mathrm{....}$

Here,

  $a=-6$

  $d=-4+6=-2+4=2$

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

  $\begin{array}{l}{t}_n=-6+\left(n-1\right)\left(2\right)\\ t_n=-6+2n-2\\ t_n=2n-6\end{array}$

Also,67^thterm of sequence is calculated as

  $\begin{array}{l}{t}_{67}=2\left(67\right)-6\\ t_{67}=134-6\\ t_{67}=128\end{array}$

Conclusion:

Hence, Sequence is described by equation $t_n=2n-6$ and $t_{67}=128$