Arithmetic Sequence Calculator — nth Term and Sum
Find the nth term and sum of an arithmetic sequence from the first term and common difference. Formulas a_n = a₁ + (n−1)·r and Sₙ. Free math calculator.
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Linear Equation Calculator
This linear equation calculator instantly solves equations of the form ax + b = c for any real coefficients. Simply enter the values of a, b, and c to get the solution for x along with automatic verification. Ideal for students, teachers, and anyone who needs to quickly solve or check linear algebra equations.
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How to use the calculator?
Enter coefficient a (the multiplier of x) — it must not be zero. Enter the constant b. Enter the right-hand side value c. The calculator instantly computes x = (c − b) / a and verifies the result by substituting x back into the equation.
Calculation Example
Solving 2x − 4 = 0: a = 2, b = −4, c = 0. We compute x = (c − b) / a = (0 − (−4)) / 2 = 4 / 2 = 2. Verification: 2 · 2 + (−4) = 4 − 4 = 0 = c. The solution x = 2 is correct.
Frequently Asked Questions
What is a linear equation?
A linear equation is a first-degree equation of the form ax + b = c, where a, b, and c are constants and x is the unknown. The solution is the value of x that satisfies the equation.
How does the calculator solve the equation?
The calculator uses the formula x = (c − b) / a. It moves constant b to the right side and divides by coefficient a to find the value of x.
What happens when a = 0?
When a = 0, division by zero is impossible and the equation has no unique solution. The calculator will indicate that no solution exists.
Can I enter negative numbers?
Yes, all fields accept negative and decimal numbers. For example, you can enter a = −3, b = 7.5, or c = −12.
What does the verification result mean?
The verification shows the value of the left side ax + b after substituting the computed x. It should equal c. If it does, the solution is correct.
Is this calculator suitable for school students?
Yes, the calculator is easy to use and presents results in a clear format. It helps students understand the method for solving linear equations.
How many decimal places does the result have?
The calculator rounds results to 6 decimal places, which provides sufficient accuracy for most mathematical applications.
Does the calculator solve systems of equations?
No, the calculator only solves single linear equations with one unknown. A different tool is needed for systems of equations.
What are the applications of linear equations?
Linear equations are the foundation of algebra and are applied in physics, economics, statistics, and programming to model linear relationships.
How can I verify the result manually?
Substitute the computed x into the equation: calculate a · x + b and check if the result equals c. This simple arithmetic check is accessible to anyone.
Results are for informational purposes only. The calculator solves only first-degree equations of the form ax + b = c with a ≠ 0. If a = 0, the equation has no unique solution.
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