Chapter 8.2, Problem 11E

a.

To determine

To calculate: The arithmetic sequence.

Answer to Problem 11E

The $nth$ rule is $a_n=6n-9$ and sequence is $-3,3,9,\mathrm{.....}$ .

Explanation of Solution

Given information:

The first term is $-3$ and each term is 6 less than the previous term.

Formula used:

Arithmetic difference − the difference of consecutive term is constant. The constant difference is called the common difference and is denoted by d.

Therefore,

  $d=a_{n+1}-a_n;n\ge 1$ .

The $nth$ tem of an arithmetic sequence with first term $a_1$ and common difference $d$ is given by : $a_n=a_1+(n-1)d$ .

Calculation:

According to the question ,

  $\begin{array}{l}{a}_1=-3\\ d=6\end{array}$

Therefore, the $nth$ term is

  $\begin{array}{l}=a_n=a_1+(n-1)d\\ =a_n=(-3)+(n-1)6\\ =-3+6n-6\\ =6n-9\end{array}$

The arithmetic sequence is $-3,3,9,\mathrm{.....}$

Hence, the $nth$ rule is $a_n=6n-9$ and sequence is $-3,3,9,\mathrm{.....}$ .

b.

To determine

To calculate: The arithmetic sequence.

Answer to Problem 11E

The $nth$ rule is $a_n=6n-9$ and sequence is $-3,3,9,\mathrm{.....}$ .

Explanation of Solution

Given information:

The first term is 7 and each term is 5 more than the previous term.

Formula used:

Odd numbers − are whole numbers that cannot be divided exactly into two pairs.

The difference of consecutive term is constant. The constant difference is called the common difference and is denoted by d.

Therefore,

  $d=a_{n+1}-a_n;n\ge 1$ .

The $nth$ tem of an arithmetic sequence with first term $a_1$ and common difference $d$ is given by : $a_n=a_1+(n-1)d$ .

Calculation:

According to the question ,

  $\begin{array}{l}{a}_1=7\\ d=5\end{array}$

Therefore,

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=7+(n-1)5\\ =7+5n-5\\ =5n+2\end{array}$

The sequence

  $\begin{array}{l}{a}_2=5(2)+2\\ =10+2\\ =12\\ a_3=5(3)+2\\ =15+2\\ =17\end{array}$

And so on.

The sequence is $7,12,17,\mathrm{........}$

Hence, the $nth$ rule is $a_n=5n+2$ and sequence is $7,12,17,\mathrm{.....}$ .