The pth term of an arithmetic progression (AP) is given by the formula:
𝑎𝑛 = 𝑎 + (𝑛 − 1)𝑑
where 𝑎 is the first term, 𝑛 is the term number, and 𝑑 is the common difference.

In this case, the pth term of the AP is given as 𝑝². We can substitute this value into the formula to find the first term, 𝑎.

𝑝² = 𝑎 + (𝑝 − 1)𝑑

To find the sum of the first 𝑛 terms of the AP, we can use the formula for the sum of an AP:

𝑆𝑛 = 𝑛/2(𝑎 + 𝑙)
where 𝑆𝑛 is the sum of the first 𝑛 terms, 𝑎 is the first term, 𝑙 is the last term, and 𝑛 is the number of terms.

Now, let's proceed to solve the problem step by step.

1. Finding the first term, 𝑎:
We have the equation 𝑝² = 𝑎 + (𝑝 − 1)𝑑
Since we know that the pth term is 𝑝², we can substitute this value into the equation:
𝑝² = 𝑎 + (𝑝 − 1)𝑑
𝑝² = 𝑎 + 𝑝𝑑 − 𝑑
𝑎 = 𝑝² − 𝑝𝑑 + 𝑑

2. Finding the common difference, 𝑑:
To find the common difference, we can use the formula for the pth term of the AP:
𝑝² = 𝑎 + (𝑝 − 1)𝑑
Substituting the value of 𝑎 from the previous step, we get:
𝑝² = 𝑝² − 𝑝𝑑 + 𝑑 + (𝑝 − 1)𝑑
Simplifying the equation, we have:
𝑝² = 𝑝² − 𝑝𝑑 + 𝑑 + 𝑝𝑑 − 𝑑
𝑝² = 𝑝²
This equation is true for any value of 𝑝, which means that the common difference can be any value.

3. Finding the sum of the first 𝑛 terms, 𝑆𝑛:
Using the formula for the sum of an AP, we have:
𝑆𝑛 = 𝑛/2(𝑎 + 𝑙)
Since we know the first term 𝑎, we can substitute it into the equation:
𝑆𝑛 = 𝑛/2(𝑎 + 𝑙)
𝑆𝑛 = 𝑛/2(𝑝² − 𝑝𝑑 + 𝑑 + 𝑙)
𝑆𝑛 = 𝑛/2(𝑝² + 𝑙)

Since we don't have information about the last term 𝑙, we cannot determine the exact value of