Question

Determine if each sequence is arithmetic. If so, indicate the common difference.

$$\begin{gathered} \left(a\right)-4,4,2,10,8,16,\dots \\ \left(b\right)-3,-1,1,3,5,7,\dots \\ \left(c\right)7,2,-3,-8,-13,-18,\dots \end{gathered}$$

Short answer

Part (a) The sequence is not arithmetic.

Part (b) The sequence is arithmetic.

Part (c) The sequence is arithmetic.

Step-by-step solution

Part (a) Step 1. Find the consecutive difference of the sequence.

Consider the given sequence: $\left(a\right)-4,4,2,10,8,16,\dots$

Find the difference between the consecutive terms.

$\begin{array}{rcl}4-\left(-4\right)& =& 8\\ 2-4& =& -2\\ 10-2& =& 8\\ 8-10& =& -2\\ 16-8& =& 8\end{array}$

• Since the difference of all consecutive terms is not the same.
• The sequence is not an arithmetic sequence.

Part (b) Step 1. Find the consecutive difference of the sequence.

Consider the given sequence: $\left(b\right)-3,-1,1,3,5,7,\dots$

Find the difference between the consecutive terms.

$\begin{array}{rcl}-1-\left(-3\right)& =& 2\\ 1-\left(-1\right)& =& 2\\ 3-1& =& 2\\ 5-3& =& 2\\ 7-5& =& 2\end{array}$

• Since the difference of all consecutive terms is the same.
• The common difference is d= 2.
• The sequence is an arithmetic sequence.

Part (c) Step 1. Find the consecutive difference of the sequence.

Consider the given sequence: $\left(c\right)7,2,-3,-8,-13,-18,\dots$

Find the difference between the consecutive terms.

$\begin{array}{rcl}2-7& =& -5\\ -3-2& =& -5\\ -8-\left(-3\right)& =& -5\\ -13-\left(-8\right)& =& -5\\ -18-\left(-13\right)& =& -5\end{array}$

• Since the difference of all consecutive terms is the same.
• The common difference is d= -5.
• The sequence is an arithmetic sequence.