The ratio of the 11th term to the 18th term of an AP 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 terms to the sum of the first `21` terms.

Explanation

Let'a' and 'd' be the first term and common difference respectively of the A.P.
Given that, `(a_(11))/(a_(18))=(2)/(3)`
`rArr (a+10d)/(a+17d)=(2)/(3)`
`rArr 3a+30d=2a+34d`
`a=4d " " ...(1)`
Now, `(a_(5))/(a_(21))=(a+4d)/(a+20d) " " `[from (1)]
`=(4d+4d)/(4d+20d)`
`=(8d)/(24d)=(1)/(3)=1:3`
and `(S_(5))/(S_(21))=((5)/(2)(2a+4d))/((21)/(2)(2a+20d))=(5(a+2d))/(21(a+10d)) " " `[from (1)]
`=(5(6d))/(21(14d))=(5)/(49)=5:49`