The formula for the Arithmetic Progression (A.P.) is as follows:

1. nth term of an A.P.: $a_n = a_1 + (n - 1) \cdot d$ Where:

   • $a_n$ is the nth term
   • $a_1$ is the first term
   • $d$ is the common difference
   • $n$ is the position of the term

2. Sum of the first n terms of an A.P.: $S_n = \frac{n}{2} \cdot \left( 2a_1 + (n - 1) \cdot d \right)$ Or equivalently: $S_n = \frac{n}{2} \cdot (a_1 + a_n)$ Where:

   • $S_n$ is the sum of the first $n$ terms
   • $a_1$ is the first term
   • $a_n$ is the nth term
   • $d$ is the common difference

Let me know if you'd like to explore any details or have questions!

Here are 5 related questions to expand on this:

1. How do you find the common difference in an arithmetic progression?
2. Can you derive the formula for the sum of an A.P.?
3. How would you calculate the nth term if you're given the sum of n terms?
4. What happens if the common difference $d$ is negative in an A.P.?
5. How can you solve for $n$ if you're given the first term, common difference, and a specific term?

Tip: Always check for the common difference between terms before applying the A.P. formula, as it must be constant.