Question

Penalty will be 4500 for 1st day, 12000 everyday after. And budget is only 155000. How many days can i afford? Using arithmetic progression.

Answer 1

You do not have an AP. That would require that the fine increase by a fixed amount each day. You just have a linear function where the total fines paid for x days is
y = 4500 + 12000(x-1)

Now. How much does the fine increase each day? If it is in fact 12000, then you have an AP with
a = 4500
d = 12000
so you can afford n days where
n/2 (2*4500 + (n-1)*12000) <= 155000
n <= 5.2

I suspect a typo or other mangling.