Definition of nth term in Arithmetic Progression
An nth term in an Arithmetic Progression (AP) refers to the general term of the sequence that follows a specific pattern. In an AP, each term is obtained by adding a constant value (known as the common difference) to the preceding term.

Formula for the nth term in Arithmetic Progression
The formula to find the nth term in an AP is given by:
\[ a_n = a_1 + (n - 1) \cdot d \]
Where:
- \(a_n\) is the nth term
- \(a_1\) is the first term of the sequence
- \(d\) is the common difference between consecutive terms
- \(n\) is the position of the term in the sequence

Example
Consider an AP with the first term \(a_1 = 2\) and common difference \(d = 3\). To find the 5th term of the AP, we substitute the values into the formula:
\[ a_5 = 2 + (5 - 1) \cdot 3 = 2 + 4 \cdot 3 = 2 + 12 = 14 \]
Therefore, the 5th term of the AP is 14.

Importance of nth term in Arithmetic Progression
- The nth term formula allows us to find any term in an AP without having to list out all the preceding terms.
- It helps in predicting future terms of the sequence based on the given pattern.
- The concept of nth term is crucial in various mathematical applications, such as finance, physics, and computer science.