Question 961982
this is an interesting problem.
i solve it this way.


the general equation is An = A1 + (n-1)*d


from this you get:


A4 = A1 + 3d
A8 = A1 + 7d
A9 = A1 + 8d


you are given that A4 is equal to -6.
from that you get:


-6 = A1 + 3d


you are given that the sum of A7 and A8 is equal to 72.
from that you get:


72 = A1 + 7d + A1 + 8d
combine like terms and you get:


72 = 2A1 + 15d


you now have two equations that need to be solved simultaneously.


they are:


-6 = A1 + 3d
72 = 2A1 + 15d


multiply the first equation by 2 and you get:


-12 = 2A1 + 6d
72 = 2A1 + 15d


subtract the first equation from the second equation and you get:


84 = 9d


solve for d and you get:


d = 9.333333333333333........ which is the same as (9 and 1/3).


that's your common difference.


you can confirm by using that value of d to solve for A1.
you will get A1 = -34.


you can then use A1 and d to solve for A4 and A8 and A9


you will find that A4 will be equal to -6 and the sum of A8 and A9 will be equal to 72.