Chapter 7.5, Problem 1GP

Solution

To state: The first five terms of the sequence: $a_1=3\text{and}{a}_n=a_{n-1}-7$

The resultant terms are $a_1=3,a_2=-4,a_3=-11,a_4=-18,a_5=-25$ .

Given information:

The given sequence is: $a_1=3\text{and}{a}_n=a_{n-1}-7$

Explanation:

Consider the given sequence,

  $a_n=a_{n-1}-7$

The first term of the sequence is: $a_1=3$

Now substitute 2 for n for the second term and simplify,

  $\begin{array}{c}{a}_2=a_{2-1}-7\\ =a_1-7\\ =3-7\\ =-4\end{array}$

Now substitute 3 for n for the third term and simplify,

  $\begin{array}{c}{a}_3=a_{3-1}-7\\ =a_2-7\\ =-4-7\\ =-11\end{array}$

Similarly, find the remaining 2 terms,

  $\begin{array}{c}{a}_4=a_{4-1}-7\\ =a_3-7\\ =-11-7\\ =-18\\ a_5=a_{5-1}-7\\ =a_4-7\\ =-18-7\\ =-25\end{array}$

Therefore, the first five terms are $a_1=3,a_2=-4,a_3=-11,a_4=-18,a_5=-25$ .