Common Difference:
The Common Difference Calculator is a tool designed to calculate the constant difference between consecutive terms in an arithmetic sequence. This difference, known as the "common difference," is essential for understanding the structure of arithmetic progressions, predicting future terms, and solving related mathematical problems.
Formula of Common Difference Calculator
The formula to calculate the common difference in an arithmetic sequence is:
Common_Difference = (Tn - T1) / (n - 1)
Where:
- Common_Difference is the constant difference between consecutive terms.
- Tn is the nth term of the sequence.
- T1 is the first term of the sequence.
- n is the position of the nth term.
Dependent Variable Formulas
- nth Term
Tn = T1 + (n - 1) * Common_Difference - First Term
T1 = Tn - (n - 1) * Common_Difference - Position (n)
n = [(Tn - T1) / Common_Difference] + 1
Useful Conversion Table
| Parameter | Description | Example Values/Notes |
|---|---|---|
| Common Difference | The constant difference (d) | Typically an integer or decimal number |
| First Term (T1) | The starting term of the sequence | Example: 3, 5, 10 |
| nth Term (Tn) | The term at position n | Example: 15, 23, 50 |
| Position (n) | The index of a term in the sequence | Example: 1, 2, 10 |
Example of Common Difference Calculator
An arithmetic sequence starts with 5, and the 10th term is 50. Calculate the common difference, the nth term for n=15, and the first term.
- Calculate the Common Difference:
Common_Difference = (Tn - T1) / (n - 1)
Common_Difference = (50 - 5) / (10 - 1) = 45 / 9 = 5 - Find the nth Term for n=15:
Tn = T1 + (n - 1) * Common_Difference
T15 = 5 + (15 - 1) * 5 = 5 + 70 = 75 - Confirm the First Term:
T1 = Tn - (n - 1) * Common_Difference
T1 = 50 - (10 - 1) * 5 = 50 - 45 = 5
The common difference is 5, the 15th term is 75, and the first term is confirmed as 5.
Most Common FAQs
The common difference is the constant value added (or subtracted) to each term in an arithmetic sequence to get the next term.
Yes, the common difference can be negative, resulting in a decreasing arithmetic sequence.
The Common Difference Calculator simplifies solving arithmetic progression problems, making it an essential tool for students, educators, and professionals in fields like finance and engineering.