Answer & Solution
Answer: Option B
Solution:
$$\eqalign{
& {18^{{\text{th}}}}\,{\text{term}}:{11^{{\text{th}}}}\,{\text{term}} = 3:2 \cr
& \Rightarrow \frac{{{a_{18}}}}{{{a_{11}}}} = \frac{3}{2} \cr
& \Rightarrow \frac{{a + 17d}}{{a + 10d}} = \frac{3}{2} \cr
& \Rightarrow 2a + 34d = 3a + 30d \cr
& \Rightarrow 34d - 30d = 3a - 2a \cr
& \Rightarrow a = 4d \cr
& {\text{Now,}} \cr
& \frac{{{a_{21}}}}{{{a_5}}} = \frac{{a + 20d}}{{a + 4d}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{4d + 20d}}{{4d + 4d}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{24d}}{{8d}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{3}{1} \cr
& \therefore {a_{21}}:{a_5} = 3:1 \cr} $$