Chapter SH, Problem 8.2.10EP

To determine

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

Answer to Problem 8.2.10EP

Sequence is described by equation $t_n=1+2n$ and $t_{99}=199$

Explanation of Solution

Given information:Sequence is $3,5,\mathrm{7....}$ and term is $99th$

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:

  $3,5,\mathrm{7....}$

Here,

  $a=3$

  $d=5-3=7-5=2$

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

  $\begin{array}{l}{t}_n=3+\left(n-1\right)\left(2\right)\\ t_n=3+2n-2\\ t_n=1+2n\end{array}$

Also,99^thterm of sequence is calculated as

  $\begin{array}{l}{t}_{99}=1+2\left(99\right)\\ t_{99}=1+198\\ t_{99}=199\end{array}$

Conclusion:

Hence, Sequence is described by equation $t_n=1+2n$ and $t_{99}=199$