Chapter 12, Problem 11RE

a.

To determine

To find the first five terms of the sequence.

Answer to Problem 11RE

7,9,11, 13, 15

Explanation of Solution

Given information:

  $a_n=2n+5$

Calculation:

Substitute $n=1,2,3,4,5$ in the given sequence and evaluate the expression to find the first five terms as shown below.

  $\begin{array}{l}{a}_1=2\cdot 1+5=7\\ a_2=2\cdot 2+5=9\\ a_3=2\cdot 3+5=11\\ a_4=2\cdot 4+5=13\\ a_5=2\cdot 5+5=15\end{array}$

b.

To determine

To graph the terms found in part (a).

Explanation of Solution

Given information:

  $a_n=2n+5$

Graph:

The terms found in part (a) are 7,9,11, 13, 15. These can be graphed as shown below.

  

c.

To determine

To find the fifth partial sum of the sequence.

Answer to Problem 11RE

55

Explanation of Solution

Given information:

  $a_n=2n+5$

Calculation:

The first five terms of the sequence are:

  $\begin{array}{l}{a}_1=7\\ a_2=9\\ a_3=11\\ a_4=13\\ a_5=15\end{array}$

So, the fifth partial sum is;

  $\begin{array}{c}{S}_5=a_1+a_2+a_3+a_4+a_5\\ =7+9+11+13+15\\ =55\end{array}$

d.

To determine

To find the fifth partial sum of the sequence.

Answer to Problem 11RE

Arithmetic, common difference is 2.

Explanation of Solution

Given information:

  $a_n=2n+5$

Calculation:

The first five terms of the sequence are:

  $\begin{array}{l}{a}_1=7\\ a_2=9\\ a_3=11\\ a_4=13\\ a_5=15\end{array}$

Observe that $a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=2$ .

Since each term differs by 2, the given sequence is arithmetic with common difference of 2.