Arithmetic Sequence Calculator with Steps
What is an Arithmetic Sequence?
An arithmetic sequence is a list of numbers where the difference between any two consecutive terms is constant. This constant value is known as the "common difference" (denoted as d). For example, in the sequence 2, 5, 8, 11..., the common difference is 3 because 5 - 2 = 3 and 8 - 5 = 3.
Understanding the Arithmetic Sequence Formulas
To find any specific term in a sequence or calculate the total sum, we use two primary formulas:
- n-th Term Formula: aₙ = a₁ + (n - 1)d
- Sum of n Terms Formula: Sₙ = (n / 2) * (2a₁ + (n - 1)d)
Where a₁ is the first term, d is the common difference, and n is the position of the term you want to find.
How to Use This Calculator
Using our Arithmetic Sequence Calculator with steps is simple. Follow these steps to get your results instantly:
- Enter the First Term (a₁): This is the starting number of your sequence.
- Enter the Common Difference (d): This is the amount added to each term to get the next one.
- Enter the Number of Terms (n): Tell the calculator how many terms you want to evaluate or sum.
- Click Calculate: View the sequence, the specific n-th term, the total sum, and a detailed step-by-step breakdown of the math involved.
Frequently Asked Questions
Q: Can the common difference be negative?
A: Yes! A negative common difference means the sequence is decreasing (e.g., 10, 7, 4, 1...).
Q: What happens if the common difference is zero?
A: If d = 0, every term in the sequence remains the same as the first term.
Q: Is an arithmetic sequence the same as a geometric sequence?
A: No. In an arithmetic sequence, you add a constant. In a geometric sequence, you multiply by a constant (ratio).