Calculating the total cost of a monthly subscription plan might sound easy, but it can be tricky because of several factors.

First, let's talk about what an arithmetic sequence is. It's when there is a constant difference between each part of a series. For a subscription plan, if the cost stays the same every month, you could use a formula to find the total cost. But in reality, most subscription plans change over time. The price might go up, there could be special discounts, or you might face extra fees. These changes make it hard to use a simple arithmetic sequence.

Next, there’s a formula used to find the total of the first $n$ parts of an arithmetic sequence:

$$S_n = \frac{n}{2} (a + l)$$

In this formula:

• $S_n$ is the total for the first $n$ months.
• $a$ is the starting cost.
• $l$ is the final cost after $n$ months.

In a subscription situation, figuring out $l$ (the last cost) and $n$ (number of months) can be difficult.

Also, if the price changes every month, then we're not really looking at a true arithmetic sequence. So, it doesn't work to just plug numbers into the formula.

To get a clearer picture, it's better to track the subscription costs each month. Write down any changes in price, and then add them up as you go. You could also create a more complex model that takes into account all the changing costs.

While looking at arithmetic sequences can help with steady pricing, it’s important to remember that they have limits when things vary, which is common in the real world.