The ratio of 6th and 8th term of an A.P. is 7:9. Find the ratio of 9th term to 13th term.
Solution :
t6 : t8 = 7 : 9
t6 / t8 = 7 / 9
(a + 5d) / (a + 7d) = 7/9
9(a + 5d) = 7(a + 7d)
9a + 45d = 7a + 49d
9a - 7a + 45d - 49d = 0
2a - 4d = 0
a - 2d = 0
a = 2d
ratio of 9th term to 13th term
t9 : t13 = (a + 8d) / (a + 12d)
= (2d + 8d) / (2d + 12d)
= 10d / 14d
= 5 / 7
= 5 : 7
Hence the ratio of 9th term to 13th term is 5 : 7.