Chapter 11.3, Problem 28WE

To determine

To calculate:

The sequence for the following condition and categorize it as arithmetic or geometric series by estimating the value of $n^{th}$ term:

Sequence of odd integers greater than two

Answer to Problem 28WE

The sequence is defined as $3,5,7,9,\mathrm{.......}$ and $n^{th}$ term is $a_n=2n$ .

Explanation of Solution

Given information:

Sequence of odd integers greater than two

Calculation:

Know that:

The Sequence of odd integers greater than two is written as:

  $3,5,7,9,\mathrm{.......}$

So, here terms are considered as:

  $\begin{array}{l}{a}_1=3\\ a_2=5\\ a_3=7\\ a_4=9\end{array}$

Check for the arithmetic sequence:

  $\begin{array}{l}d=a_2-a_1=5-3=2\\ d=a_3-a_2=7-5=2\\ d=a_4-a_3=9-7=2\end{array}$

Here, common difference is same $2$ . Therefore, the given sequence is arithmetic sequence. Now, the $n^{th}$ term is calculated as:

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ a_n=2+\left(n-1\right)\left(2\right)\\ a_n=2+2n-2\\ a_n=2n\end{array}$