1. The ratio of the 11th term to the 18th term of an A.P. is 2:3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five term to the sum of the first 21 terms.

@Vikas: Good efforts..!!

Here is the proper solution.

Let a and d be the first term and the common difference of the A.P.

It is given that

⇒ 3 (a + 10d) = 2 (a + 17d)  [∵ an = a + (n – 1)d]

⇒ 3a + 30d = 2a + 34d

⇒ 3a – 2a = 34d – 30d 

 

To find: (1) a5 : a21     (2) S5 : S21 

(1) a5 : a21 

Thus, a5 : a21 = 1 : 3

 

(2)

Thus, S5 : S21 = 5 : 49

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A.T.Q

a + 10d/a + 17d = 2/3

3(a + 10d) = 2(a + 17d)

3a + 30d = 2a + 34d

a = 4d ......(i)

we have to find

(i) a + 4d/a + 20d = 8d/24d = 1/3

(ii) { 5/2(2a + 4d)} / { 5/2(2a + 20d) } = (2a + 4d)/(2a + 20d) = 12d/28d = 3/7

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