Precalculus (6th Edition) Blitzer

$-1,1,3,5,7,...$ Arithmetic.
After observing the sequence carefully, we notice that the difference between two consecutive terms is the same. $-1,1,3,5,7,...$ Here, ${{a}_{1}}=-1,{{a}_{2}}=1,{{a}_{3}}=3,{{a}_{4}}=5,{{a}_{5}}=7,...$ So, \begin{align} & {{a}_{2}}-{{a}_{1}}=1-\left( -1 \right) \\ & =2 \\ & {{a}_{3}}-{{a}_{2}}=3-1 \\ & =2 \end{align} \begin{align} & {{a}_{4}}-{{a}_{3}}=5-3 \\ & =2 \\ & {{a}_{5}}-{{a}_{4}}=7-5 \\ & =2 \end{align} Therefore, the common difference is 2. Hence, the sequence is Arithmetic.