Question

the ratio of the 11th term to the 18th term of an ap is2:3.Find the ratio of the 5th term to the 21th term,and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Answer 1

a_{11}/ a_{18}
a+10d/a+17d =2/3
2(a+17d) =3(a+10d)
2a+34d =3a+30d
4d=a
Then,a_{5} / a_{21} 
= a+4d/a+20d
= 4d+4d/20d+4d
= 8d/24d
= d/3d
= 1/3
So. ratio is 1:3