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Question
The ratio of 6th and 8th term of an A.P. is 7:9. Find the ratio of 9th term to 13th term
Solution
`("t"_6)/("t"_8) = 7/9`
`("a" + 5"d")/("a" + 7"d") = 7/9`
9a + 45d = 7a + 49d
9a + 45 – 7d = 7a + 49d
9a + 45d – 7a – 49d = 0
2a – 4d = 0 ⇒ 2a = 4d
a = 2d
Substitue a = 2d in
`("t"_9)/("t"_13) = ("a" + 8"d")/("a" + 12"d")`
= `(2"d" + 8"d")/(2"d" + 12"d")`
= `(10"d")/(14"d")`
= `5/7`
t9:t13 = 5:7
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