Chapter 8.5, Problem 4E

To determine

To write: the first six terms of the given sequence.

Answer to Problem 4E

  $1,-4,-9,-14,-19,-24$ .

Explanation of Solution

Given:

The given sequence is $a_n=a_{n-1}-5$ .

  $a_1=1$

Calculation:

According to the given sequence, $a_n=a_{n-1}-5$ .

Therefore, the first six terms of the given sequence are $a_2,a_3,a_4,a_5,a_6$ .

Now, to find the first six terms of the given sequence is given by

  $\begin{array}{l}{a}_n=a_{n-1}-5\{\text{given sequence}}\\ a_2=a_{2-1}-5\{\text{put }n=2\text{}}\\ a_2=a_1-5\\ a_2=1-5=-4\{\text{substitutes }{a}_1=1\text{}}\\ a_3=a_{3-1}-5\{\text{put }n=3\text{}}\\ a_3=a_2-5\\ a_3=-4-5=-9\{\text{substitutes }{a}_2=-4\text{}}\end{array}$

  $\begin{array}{l}{a}_4=a_{4-1}-5\{\text{put }n=4\text{}}\\ a_4=a_3-5\\ a_4=-9-5=-14\{\text{substitutes }{a}_3=-9\text{}}\\ a_5=a_{5-1}-5\{\text{put }n=5\text{}}\\ a_5=a_4-5\\ a_5=-14-5=-19\{\text{substitutes }{a}_4=-14\text{}}\\ a_6=a_{6-1}-5\{\text{put }n=5\text{}}\\ a_6=a_5-5\\ a_6=-19-5=-24\{\text{substitutes }{a}_5=-19\text{}}\end{array}$

Hence, the first six terms of the given sequence are $1,-4,-9,-14,-19,-24$ .