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.