91Ó°ÊÓ

Consider the given sequence: $\left(a\right)9,20,31,42,53,64,…$

Find the difference between the consecutive terms.

$\begin{array}{rcl}20-9& =& 11\\ 31−20& =& 11\\ 42−31& =& 11\\ 53−42& =& 11\\ 64−53& =& 11\end{array}$

• Since the difference of all consecutive terms is the same.
• The common difference is d= 11.
• The sequence is an arithmetic sequence.

Consider the given sequence:$\left(b\right)12,6,0,−6,−12,−18$

Find the difference between the consecutive terms.

$\begin{array}{rcl}6-12& =& -6\\ 0-6& =& -6\\ -6-0& =& -6\\ -12-\left(-6\right)& =& -6\\ -18-\left(-12\right)& =& -6\end{array}$

• Since the difference of all consecutive terms is the same.
• The common difference is d= -6.
• The sequence is an arithmetic sequence.

Consider the given sequence: $\left(c\right)7,1,10,4,13,7,…$

Find the difference between the consecutive terms.

$\begin{array}{rcl}1-7& =& -6\\ 10-1& =& 9\\ 4-10& =& -6\\ 13-4& =& 9\\ 7-13& =& -6\end{array}$

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