Chapter 4.6, Problem 40E

To determine

To describe and correct: the error in the given arithmetic sequence

Answer to Problem 40E

Therefore, the $n^{\text{th }}$ term of the sequence $2,1,0,-1,\dots$ is $\left[a_n=14+8n\right]$

Explanation of Solution

Given:

The sequence corresponding to the figure is $14,22,30,38,\dots$

Calculation:

The sequence corresponding to the figure is $14,22,30,38,\dots$

Now, check the difference between terms

So,

  $22-14=8$

  $30-22=8$

  $38-30=8$

Thus, there is a common difference between terms is 8

The first term of the sequence is $a_0=14$

So, the $n^{\text{th }}$ term of the sequence is

  $a_n=a_0+nd$

Put the values $a_0=14$ and $d=8$

  $a_n=14+8n$

Therefore, the $n^{\text{th }}$ term of the sequence $2,1,0,-1,\dots$ is $\left[a_n=14+8n\right]$

Conclusion:

Therefore, the $n^{\text{th }}$ term of the sequence $2,1,0,-1,\dots$ is $\left[a_n=14+8n\right]$