the ratio of the 5th and 3rd terms of an AP is 2.5 find the ratio of the 15th and 7th terms
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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
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
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