The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If n^th term is the largest negative term, what is the value of n ? 

For how many integral values of k, the equation x² - 4x + k = 0, where k is an integer has real roots and both of them lie in the interval (0, 5) ? 

In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms ?

Consider the following statements :

1. (25)! + 1 is divisible by 26

2. (6)! + 1 is divisible by 7

Which of the above statements is/are correct ?