The 4th term of an A.P is 6. if the sum of 8 and 9th terms is -72, find the common difference
In AP:
an = a - ( n - 1 ) d
where
a = first term
d = common difference
In this case:
a4 = a + 3 d
a4 = 6
a + 3 d = 6
a8 = a + 7 d
a9 = a + 8 d
a8 + a9 = - 72
a + 7 d + a + 8 d = - 72
2 a + 15 d = - 72
Now you must solve system of two equations.
a + 3 d = 6
2 a + 15 d = - 72
The solutions are:
a = 34 , d = - 28 / 3