Chapter 9, Problem 31RE

Solution

To state: The first six terms and the 12^th term of the arithmetic sequence:

  $a_1=-5\text{and}d=1.5$ .

The resultants first six terms are $-5,-3.5,-2,-0.5,1,2.5$ and the 12^th term is $11.5$ .

Given information:

The given values are $a_1=-5\text{and}d=1.5$ .

Explanation:

The first term of the sequence is: $a_1=-5$

The common difference is: 1.5

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

  $\begin{array}{c}{a}_2=a_1+1.5\\ =-5+1.5\\ =-3.5\end{array}$

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

  $\begin{array}{c}{a}_3=a_2+1.5\\ =-3.5+1.5\\ =-2\end{array}$

Similarly, find the remaining 3 terms,

  $\begin{array}{c}{a}_4=a_3+1.5\\ =-2+1.5\\ =-0.5\\ a_5=a_4+1.5\\ =-0.5+1.5\\ =1\\ a_6=a_5+1.5\\ =1+1.5\\ =2.5\end{array}$

Similarly, the 12^th term is:

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ a_{12}=-5+\left(12-1\right)1.5\\ =-5+11\cdot \left(1.5\right)\\ =-5+16.5\\ =11.5\end{array}$

Therefore, the first six terms are $-5,-3.5,-2,-0.5,1,2.5$ and the 12^th term is $11.5$ .