Chapter 8.5, Problem 3E

To determine

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

Answer to Problem 3E

  $1,4,7,10,13,16$ .

Explanation of Solution

Given:

The given sequence is $a_n=a_{n-1}+3$ .

  $a_1=1$

Calculation:

According to the given sequence, $a_n=a_{n-1}+3$ .

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

  $\begin{array}{l}{a}_n=a_{n-1}+3\{\text{given sequence}}\\ a_2=a_{2-1}+3\{\text{put }n=2\text{}}\\ a_2=a_1+3\\ a_2=1+3=4\{\text{substitutes }{a}_1=1\text{}}\\ a_3=a_{3-1}+3\{\text{put }n=3\text{}}\\ a_3=a_2+3\\ a_3=4+3=7\{\text{substitutes }{a}_2=4\text{}}\end{array}$

  $\begin{array}{l}{a}_4=a_{4-1}+3\{\text{put }n=4\text{}}\\ a_4=a_3+3\\ a_4=7+3=10\{\text{substitutes }{a}_3=7\text{}}\\ a_5=a_{5-1}+3\{\text{put }n=5\text{}}\\ a_5=a_4+3\\ a_5=10+3=13\{\text{substitutes }{a}_4=10\text{}}\\ a_6=a_{6-1}+3\{\text{put }n=5\text{}}\\ a_6=a_5+3\\ a_6=13+3=16\{\text{substitutes }{a}_5=13\text{}}\end{array}$

Hence, the first six terms of the given sequence are $1,4,7,10,13,16$ .