An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference, and it remains the same throughout the sequence.
The common difference in an arithmetic progression can be calculated by subtracting any term from its preceding term. This means that if the first term is 'a' and the second term is 'b', then the common difference is (b-a).
The formula for finding the nth term in an arithmetic progression is: a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
To determine if a sequence is an arithmetic progression, you can check if the difference between any two consecutive terms is the same. If the difference is constant, then the sequence is an arithmetic progression.
The sum of an arithmetic progression can be calculated using the formula: (n/2)(2a + (n-1)d), where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms in the sequence.