The 8th term of an Ap is 5 times the 3rd while the 7th term is 9 greater than the fourth. Write the first five terms of the Ap
Simply use your definitions to translate:
"The 8th term of an Ap is 5 times the 3rd" ---> a+7d = 5(a+2d)
a+7d = 5a + 10d
-4a = 3d
a = -3d/4
"the 7th term is 9 greater than the fourth" ---> a+6d > a+3d by 9
a+6d = a+3d + 9
3d = 9
d = 3
since a = -3d/4
a = -3(3)/4 = -9/4
So the sequence is -9/4, 3/4, 15/4, 27/4, 39/4, ...
I will leave it up to you to check my arithmetic.