Sum of a part arithmatic and part geometric sequence

Please Help me.

Sequence Question

There are 4 positive numbers in a sequence. The first three are in Arithmatic sequence and the last three are in geometric sequence. If the difference between the last number and the first number is 30. What is the sum of the 4 numbers?

A1 A2 A3 A4

A1 A2 A3 are in arithmatic sequence

A2 A3 A4 are in geometric sequence

A4 - A1 = 30

What is the sum of all four terms?

Thank you for your response

I have checked the question and that was it. I have tried your method and failed. So I tried to work with b (2nd term) and c (3rd term) being both Arithmatic and Geometric and it put me in circles. I'm not sure how to go around this. Maybe we can just find the sum without actually getting the individual terms? I'm working on that right now but nothing yet.