If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
A. 3 : 2
B. 3 : 1
C. 1 : 3
D. 2 : 3
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {18^{{\text{th}}}}\,{\text{term}}:{11^{{\text{th}}}}\,{\text{term}} = 3:2 \cr & \Rightarrow \frac{{{a_{18}}}}{{{a_{11}}}} = \frac{3}{2} \cr & \Rightarrow \frac{{a + 17d}}{{a + 10d}} = \frac{3}{2} \cr & \Rightarrow 2a + 34d = 3a + 30d \cr & \Rightarrow 34d - 30d = 3a - 2a \cr & \Rightarrow a = 4d \cr & {\text{Now,}} \cr & \frac{{{a_{21}}}}{{{a_5}}} = \frac{{a + 20d}}{{a + 4d}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{4d + 20d}}{{4d + 4d}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{24d}}{{8d}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{3}{1} \cr & \therefore {a_{21}}:{a_5} = 3:1 \cr} $$Related Questions on Progressions
Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.
A. 5
B. 6
C. 4
D. 3
E. 7
The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is
A. 600
B. 765
C. 640
D. 680
E. 690
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