Question

The ratio of a11 to a18 is 2/3 then find the ratiobod a5 to a21 and ratio of sum if a5 to a21

Answer 1

a11/a18 = 2/3

3*a11 = 2*a18

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

3a+30d = 2a+34d

a = 4d

a5/a21 = (a+4d)/(a+20d)

           = (a+a)/(a+5a)    since a=4d

           = (2a)/(6a)

           = 1:3

Answer 2

Answer:

a5 : a21 = 1 : 3

s5 : s21 = 5 : 49

Step-by-step explanation:

a11:a18 = 2:3

3(a11)=2(a18)

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

3a +30d = 2a + 34d

3a-2a = 34d - 30d

a = 4d

now , a5:a21

can be written as  , a + 4d : a + 20d

substituting a =4d

4d + 4d : 4d +20d

8d : 24d

1 : 3

a5 : a21 = 1 : 3

s5 : s21= 5/2(2a+4d) : 21/2 (2a+20d)

              substituting we get

5/2(2<4d> +4d) : 21/2 (2<4d> + 20d)

5/2(8d+4d) : 21/2(8d+20d)

5/2(12d) : 21/2(28d)

30d : 294d

ie. 5: 49

therefore , s5 : s21 = 5 :49

HOPE  IT  HELPED !!!