I need to calculate a membership cost.
The first year's membership will be £530, the second year will be £530 + £25, so £555.Every year, the renewal will be an additional £25, so year one = 530, year two = 555, year 3 = 580 and so on.
I need to calculate, based on how long the membership will be, wat the total cot of that membership will be i.e. if it were a 3 year membership it would be 530 + 555 + 580.
Shy of working out each year's cost, then adding them all together, is there a formula I can use to work this out? I'll need to program this into a query, so need the specific equation.
Hint-1: Suppose the first year's membership was $0$ and the membership rose by $1$ each year. What would the cost be after $n$ years.
Related question: What is the formula for $1 + 2 + \cdots + (n-1)$?
Hint-2: Suppose the first year's membership was $0$ and the membership rose by $k$ each year. How has that affected the answer given to Hint-1?
Hint-3: Suppose the first year's membership was $n$ and the membership rose by $k$ each year. How has that affected the answer given to Hint-2?