Find the 37th term of the AP

The given AP can be rewritten as 6, 31/4 ,19/2 , 45/4,…

Here, First term = a = 6

Common difference = d = (31/4) - 6 = 7/4

To find = 37^th term, ∴ n = 37

Using the formula for finding n^th term of an A.P.,

a_n = a + (n - 1) × d

∴ a_n = 6 + (37 - 1) × (7/4)

⇒ a_n = 6 + 36 × (7/4) = 6 + 63 = 69

∴ 37^th term of the given AP is 69.