Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220 . If the second term in it is 12 , then its 4 th term is :

Step-by-step solution

Given that 200 < S 9 < 220 As we know sum of n terms of A.P whose first term is a and common difference d is S n = n 2 2 a + n - 1 d ⇒    200< 9 2 2 a + 8 d < 220 ⇒    2 0 0 9 < a + 4 d < 2 2 0 9 As we know n t h term of A.P is T n = a + n - 1 d Also T 2 = a + d = 1 2 ⇒    4 d = 48 - 4 a ∴    2 0 0 9 < a + 48 - 4 a < 2 2 0 9 ⇒    2 0 0 9 - 4 8 < - 3 a < 2 2 0 9 - 4 8 &#865