The Sequence Formula Calculator is a versatile tool designed to solve arithmetic progression problems instantly. Whether you are finding the nth term, the starting value, or the common difference, this calculator provides precise results with detailed logical steps.
Sequence Formula Calculator
Sequence Formula Calculator Formula:
Source: Khan Academy Arithmetic Sequences & Wolfram MathWorld
Variables:
- an: The value of the specific term at position n.
- a1: The starting value or first term of the sequence.
- d: The constant amount added to each term (common difference).
- n: The position of the term in the sequence (must be a positive integer).
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What is a Sequence Formula Calculator?
An arithmetic sequence is a list of numbers where the difference between consecutive terms is constant. The sequence formula calculator uses the standard linear equation to find missing parts of a progression. This is fundamental in algebra, physics for uniform motion, and finance for simple interest calculations.
By inputting known variables like the starting term and the rate of change, users can predict future values or backtrack to find the origin of a data series.
How to Calculate (Example):
- Identify your known variables. For example: a1 = 10, d = 5, n = 8.
- Plug them into the formula: an = 10 + (8 – 1) * 5.
- Simplify the parenthesis: an = 10 + (7) * 5.
- Perform multiplication: an = 10 + 35.
- Find the final sum: an = 45.
Frequently Asked Questions (FAQ):
What if the common difference is negative?
If d is negative, the sequence is decreasing. The formula still works perfectly; just ensure you use the negative sign in your calculations.
Can “n” be a decimal?
No. In standard sequences, “n” refers to the position (1st, 2nd, 3rd…), so it must always be a positive integer.
Is this for Geometric sequences?
No, this specifically calculates Arithmetic Sequences (addition/subtraction). Geometric sequences require a ratio formula (multiplication).
What if I know the sum?
If you have the sum of the sequence, you would need the Arithmetic Series formula, which is a variation of this calculation.