Chapter 8, Problem 25CR

To determine

To find: The first five terms of the arithmetic sequence and find the common difference and write the $n\text{th}$ terms of the sequence.

Answer to Problem 25CR

The first five terms of the given arithmetic sequence are $35,32,29,26,23$ .

The $n\text{th}$ term of the given sequence is $a_n=35-3\left(n-1\right)$ .

Explanation of Solution

Given information:$$

  $a_1=35,a_{k+1}=a_k-3$

From the equation $a_{k+1}=a_k-3$ , we can say that each subsequent term in the sequence is subtracted by $3$ from the previous term. So the common difference $d=3$ .

Finding the first five terms,

  $\begin{array}{l}{a}_1=35\\ a_2=a_1-3=35-3=32\\ a_3=a_2-3=32-3=29\\ a_4=a_3-3=29-3=26\\ a_5=a_4-3=26-3=23\end{array}$

Finding the $n\text{th}$ term,

  $a_n=35-3\left(n-1\right)$

Thus we can find the first five terms and the $n\text{th}$ term of the given arithmetic sequence.