#### Question

Seven numbers a_1, a_2, a_3, a_4, a_5, a_6 and a_7 form an arithmetic sequence, where a_1 < a_2 < a_3 < a_4 < a_5 < a_6 < a_7. It is given that the mean of the seven numbers is 0.

Find a_4.

If the number a_4 is deleted, is there any change in the variance of the numbers? Explain your answer.