Chapter 4.7, Problem 2P

a.

To determine

whether the sequence is arithmetic and if it is ,then find common difference.

Answer to Problem 2P

The sequence is not arithmetic.

Explanation of Solution

Given sequence: $8,15,22,30,\mathrm{.....}$

Calculation:

If each term of given sequence after the first term is obtained by adding the previous one by a fixed constant, then the sequence is an arithmetic sequence and the fixed constant is common difference.

Now,

  $\begin{array}{l}15-8=7,\\ 22-15=7,\\ 30-22=8\end{array}$

Since difference between two consecutive terms is not fixed.

Therefore, the sequence is not arithmetic.

b

To determine

whether the sequence is arithmetic and if it is ,then find common difference..

Answer to Problem 2P

The sequence is arithmetic and the common difference is 2.

Explanation of Solution

Given sequence: $7,9,11,13$

Calculation:

If each term of given sequence after the first term is obtained by adding the previous one by a fixed constant, then the sequence is an arithmetic sequence and the fixed constant is common difference.

Now,

  $\begin{array}{l}9-7=2\\ 11-9=2\\ 13-11=2\end{array}$

Since difference between two consecutive terms is fixed constant and the fixed constant is 2.

Therefore, the sequence is arithmetic and the common difference is 2.

c.

To determine

whether the sequence is arithmetic and if it is ,then find common difference.

Answer to Problem 2P

The sequence is arithmetic and the common difference is $-6$ .

Explanation of Solution

Given sequence: $10,4,-2,-8,\mathrm{.....}$

Calculation:

If each term of given sequence after the first term is obtained by adding the previous one by a fixed constant, then the sequence is an arithmetic sequence and the fixed constant is common difference.

Now,

  $\begin{array}{l}4-10=-6\\ -2-4=-6\\ -8-\left(-2\right)=-6\end{array}$

Since difference between two consecutive terms is fixed constant and the fixed constant is $-6$ .

Therefore, the sequence is arithmetic and the common difference is $-6$ .

d

To determine

whether the sequence is arithmetic and if it is ,then find common difference.

Answer to Problem 2P

The sequence is not arithmetic

Explanation of Solution

Given sequence: $2,-2,2,-2,\mathrm{....}$

Calculation:

If each term of given sequence after the first term is obtained by adding the previous one by a fixed constant, then the sequence is an arithmetic sequence and the fixed constant is common difference.

Now,

  $\begin{array}{l}-2-2=-4\\ 2-\left(-2\right)=4\\ -2-2=-4\end{array}$

Since difference between two consecutive terms is not fixed.

Therefore, the sequence is not arithmetic.