The number of terms in an A . P . is even, the sum of the odd terms in it is 24 and that the even terms is 30 . If the last term exceeds the first term by 10 1 2 , then the number of terms in the A . P . is

Step-by-step solution

We know that the n t h term and sum of n terms of an A . P . with first term a and common difference d are respectively a + n - 1 d and n 2 2 a + n - 1 d . Let, the number of terms in the given A . P . be 2 n then there are 2 n 2 = n even terms and n odd terms. Then, T 1 = a and T 2 n = a + ( 2 n - 1 ) d Given T 2 n - T 1 = 21 2 ⇒ 2 n - 1 d = 21 2 ⇒ 2 n d - d = 21 2       . . . i Also, the sum of odd terms i.e. a + a + 2 d + a + 4 d + . . . is n 2 2 a + n - 1 2 d = 24 ⇒ 2 a + n - 1