The ratio of 11th term to the 18th term of an A.P is 2:3 . Find the ratio of 5th term to the 21st term and also the ratio of sum of first five terms to the sum of first 21 terms
Answers
Answer:
i) 1 : 3 , ii) 5 : 49
Step-by-step explanation:
11th term / 18th term = 2 /3
3( 11th term ) = 2 (18th term)
3 (a + 10d) = 2 ( a + 17d)
3a + 30d = 2a + 34d
3a - 2a = 34d - 30d
a = 4d ...............(1)
5th term / 21st term = (a + 4d) / (a + 20d)
= (4d + 4d) / ( 4d + 20d)
= 8d / 24d
= 1/3
∴ ratio of 5th term to the 21st term = 1 : 3
Sum of first five terms / sum of first 21 term = { 5/2 [2a +4d] } {21/2 [2a+20d]}
= 5/2 x 2/21 (8d +4d) / (8d + 20d)
= 5/21 x (12d /28d)
=5/21 x 12/28
= 5/49
∴ ratio of sum of first 5 terms to the sum of 21st term = 5 : 49