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
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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
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