Question

The ratio of 6^th and 8^th term of an A.P. is 7:9. Find the ratio of 9^th term to 13^th term

Answer 1

`("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