If the ratio between 5th and 10h terms of an A.P. is 1:2 and 12th term

1.	If the ratio between 5th and 10h terms of an A.P. is 1:2 and 12th term is 36, find that A.P.
Answer» n'th term in ap = a + (n-1)d Thus, here, 5th term = a+4d 10th term = a+9d 12th term = a+11d Given, (a+4d) / (a+9d) = 1/2 or, 2a + 8d = a + 9d or, a = d Also given, 12th term ⇒ a + 11d = 36 or, 12d = 36 [as a=d proved previously] or, d = 3 Thus, a = 3 Therefore, the ap: 3, 6, 9, 12, 15, 18... tq

If the ratio between 5th and 10h terms of an A.P. is 1:2 and 12th term is 36, find that A.P.

Answer»

n'th term in ap = a + (n-1)d

Thus, here, 5th term = a+4d

10th term = a+9d

12th term = a+11d

Given, (a+4d) / (a+9d) = 1/2

or, 2a + 8d = a + 9d

or, a = d

Also given, 12th term ⇒ a + 11d = 36

or, 12d = 36 [as a=d proved previously]

or, d = 3

Thus, a = 3

Therefore, the ap: 3, 6, 9, 12, 15, 18...