Answer
a) Neither
b) Arithmetic sequence, next term= 3
c) Geometric sequence, next term=$9\sqrt 3$
d) Arithmetic sequence, next term= 3
Work Step by Step
a) $5-(-3)\ne -3-5$. There is no common difference. Therefore the sequence is not an arithmetic progression.
$5\div(-3)\ne -3\div5$. There is no common ratio. Therefore the sequence is not a geometric progression.
b) $\frac{7}{3}-\frac{5}{3}=\frac{5}{3}-1=1-\frac{1}{3}=\frac{2}{3}$
The given sequence is an arithmetic sequence with common difference $d=\frac{2}{3}$. Next term= $\frac{7}{3}+\frac{2}{3}=\frac{9}{3}=3$
c) $\frac{9}{3\sqrt 3}=\frac{3\sqrt 3}{3}=\frac{3}{\sqrt 3}=\sqrt 3$
The given sequence is a geometric sequence with common ratio $r=\sqrt 3$. Next term=$9\times\sqrt 3=9\sqrt 3$
d) $\frac{3}{2}-0=0-(-\frac{3}{2})=-\frac{3}{2}-(-3)=\frac{3}{2}$.
The given sequence is an arithmetic progression with common difference $d=\frac{3}{2}$. Next term=$\frac{3}{2}+\frac{3}{2}=3$.
