Step 1
Given the sequence \((a) \frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81},...\)
Common difference, \(d = t_1 − t_2 = \frac{2}{9} − \frac{1}{3} = \frac{-1}{3} \neq t_4 − t_3= \frac{-5}{81}\)
The sequence (a) is not arithmetic .
Common ratio \(r = \frac{t_2}{t_1} = \frac{3}{2} \neq \frac{7}{2} = \frac{t_3}{t_2}\)
The sequence (a) is not geometric.
The given sequence is none of the above mentioned types.
\(ul O (a)\frac{1}{3}, \frac{2}{9}, \frac{3}{27}, \frac{4}{81},...\)
Step 2
\((b) 3,8,13,18,...48\)
Common difference, \(d = t_1 − t_2 = 8 − 3 = −5 = t_3 − t_2 = 13−8 = −5= t_4 − t_3 = −5= .....\)
The given sequence (b) is arithmetic.
\(ul A (b) 3,8,13,18,...48\)