- "An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence."
A sequence of numbers where the difference between any two consecutive terms is constant.
- "The constant difference is called the common difference of that arithmetic progression."
- "For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2."
- "The n-th term of the sequence (an) is given by: an = a1 + (n-1)d"
- "A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression."
- "The sum of a finite arithmetic progression is called an arithmetic series."
- "The common difference is called the common difference of that arithmetic progression."
- Example: If the initial term (a1) is 3 and the common difference (d) is 4, find the 7th term (an). - Solution: an = a1 + (n-1)d = 3 + (7-1)4 = 3 + 6(4) = 27
- No direct quote answer, but it is possible for an arithmetic progression to have a negative common difference.
- No direct quote answer, but if you know two terms (an and an-1) of an arithmetic progression, the common difference can be calculated as d = an - an-1.
- No direct quote answer, but if the common difference is zero, the sequence would consist of repeated identical terms.
- No direct quote answer, but if you know both the initial term (a1) and the n-th term (an), the common difference can be calculated as d = (an - a1) / (n - 1).
- No direct quote answer, but an arithmetic progression can have a decreasing common difference if the difference between each term and its preceding term decreases uniformly.
- No direct quote answer.
- No direct quote answer, but 'a' represents the initial term of the arithmetic progression.
- No direct quote answer, but yes, an arithmetic progression can have a common difference of zero if the sequence consists of repeated identical terms.
- No direct quote answer. The formula to calculate the sum of a finite arithmetic progression is: Sn = (n / 2) * (2a1 + (n-1)d).
- No direct quote answer, but the initial term is denoted as a1 in the formula.
- No direct quote answer, but yes, the common difference of an arithmetic progression can be a fraction.
- No direct quote answer, but yes, an arithmetic progression can have an infinite number of terms when the sequence continues indefinitely.