Question

the ratio of 4th term to 6th term of an AP os 2:1 and it's 19th term is 80.Find the common difference of the AP​

Answer 1

Answer:

80/11

Step-by-step explanation:

Let the first term and common difference be 'a' and 'd'.

 According to the question:

19th term = 80  ⇒ a + 18d = 80

⇒ a = 80 - 18d        ...(1)

Moreover, ratio of 4th and 6th term is 2:1.

⇒ (a + 3d)/(a + 5d) = 2/1

⇒ 1(a + 3d) = 2(a + 5d)

⇒ a + 3d = 2a + 10d

⇒ 3d - 10d = 2a - a

⇒ - 7d = a

⇒ - 7d = 80 - 18d         [from (1)}

⇒ 11d = 80

⇒ d = 80/11