Question

The ratio of the 5th and 3rd term of an ap is 2.5.find the ratio of its 15th and 7th term

Answer 1

let first term =a , common difference =d of an AP
third term = a3 = a+2d 
5th term = a5 = a+4d
ratio = 2/5
(a+4d)/(a+2d) = 2/5

5(a+4d) = 2(a+2d)
5a+20d = 2a +4d
5a-2a = 4d -20d
3a= -16d
a= -16d/3 ---(1)

ratio of 15th term and 7th term = (a+14d)/(a+6d)

= [-16d/3 +14d]/[-16d/3 +6d] from (1)

= [-16d +42d]/ [ -16d +18d]
= 26d/2d
=13/1
=13:1

Answer 2

a+4d/a+2d=2.5
a+4d=2.5a+5d
-d=1.5a
15th/7th=a+14d/a+6d
=a-21a/a-9a
=-20a/-8a
=2.5