(i) 1/6, 1/3, 1/2, .... is an A.P. common difference is 1/6.
d = 1/3 - 1/6 = 2-1/ 6 = 1/6
or d = 1/2 - 1/3 = \(\frac{3-2}6\) = 1/6
\(\therefore\) a4 = a3 + d = \(\frac12 + \frac16 =
\frac{3+1}6\) = 4/6 = 2/3
(ii) a1 = 1/6, a2 = 1/3, a3 = 2/3
\(\frac{a_2}{a_1}=\cfrac{\frac13}{\frac{1}{6}}\) = \(\frac63=2\)
\(\frac{a_3}{a_2}=\cfrac{\frac23}{\frac{1}{3}}\) = 2
\(\therefore\) 1/6, 1/3, 2/3., is a G.P. whose common ratio is 2.
a4 = a3r = 2/3 x 2 = 4/3