Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............
Step-by-step explanation:
From the first statement, 
S₅ = ⁵/₂(2a + ( n - 1 )d }    = 30
        5(2a  + 4d )d           = 60
        10a    + 20d             = 60
reduce to lowest term to easy calculation by dividing through by 10
                       a + 2d       = 6 -----------------------------------1
second statement
 sum of the next 4 terms inclusive 
T₉  = ⁹/₂(2a + 8d )   = 69
         9(2a  + 8d )    = 30 + 69
             18a + 72d   = 99 x 2
             18a + 72d   = 198
divide through by 18 to reduce to lowest time
                 a  + 4d    = 11 ------------------------------------------2
Now solve the two equation simultaneously to find a and d
                  a + 2d = 6
                  a + 4d = 11
                      -2d  = -5
                           d = ⁵/₂.
Now substitute  for d to get a
                a  + 2(⁵/₂) = 6
                 a + 5       = 6 
                            a   = 6 - 5
                             a = 1.
Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............