91Ó°ÊÓ

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

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.

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

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.

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

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.