If the seventh term of an A.P. is and its ninth term is find its 63rd term.

Given, a 7 = (Eq 1) a 9 = (Eq 2) By using formula a n = a + (n - 1)d for Eq 1 we get, ⇒ a 7 = a + (7 - 1)d = ⇒ a + 6d = ⇒ 9(a + 6d) = 1 ⇒ 9a + 54d = 1 ⇒ 9a = 1 - 54d ⇒ a = (Eq 3) By using formula a n = a + (n - 1)d for Eq 2 we get, ⇒ a 9 = a + (9 - 1)d = ⇒ a + 8d = (Eq 4) Putting value of a from Eq 3 in Eq 4 above, 63rd term = a 63 = Hence, 63rd term of the A.P. is 1.