Arithmetic Progression Calculator
Calculate the Nth term and Sum of an Arithmetic Sequence with step-by-step solutions. Ideal for students learning algebra.
Step-by-Step Solution
About
Arithmetic progressions are the foundation of discrete mathematics and sequence analysis. Students and educators often require a reliable method to verify manual calculations of the Nth term and the sum of series. This tool eliminates calculation errors common when dealing with negative integers or decimals.
Understanding the stepwise derivation is critical for algebraic mastery. Rather than simply providing a final number, this calculator breaks down the substitution process into the standard formulas for the general term and the arithmetic series sum. It handles integers, floating-point numbers, and negative differences with precision.
Formulas
The Nth term of an arithmetic progression is determined by adding the common difference to the first term n-1 times:
The sum of the first n terms is calculated using the average of the first and last term, multiplied by the count:
Reference Data
| Sequence Type | Description | Example Δ | Common Formula |
|---|---|---|---|
| Increasing | Terms grow larger; positive difference (d > 0). | 2, 5, 8, 11 (d = 3) | an = a1 + (n−1)d |
| Decreasing | Terms grow smaller; negative difference (d < 0). | 10, 8, 6, 4 (d = -2) | an = a1 + (n−1)(−d) |
| Constant | Terms remain unchanged; difference is zero. | 5, 5, 5, 5 (d = 0) | Sn = n × a1 |
| Finite | A sequence with a fixed number of terms. | {1, 3, 5, 7} | Domain: 1 ≤ n ≤ N |
| Infinite | A sequence that continues indefinitely. | {2, 4, 6...} | n → ∞ |
| Gauss's Sum | Sum of first 100 integers. | 1 to 100 | S100 = 5050 |
| Odd Numbers | Sum of the first n odd numbers. | 1, 3, 5... | Sn = n2 |
| Even Numbers | Sum of the first n even numbers. | 2, 4, 6... | Sn = n(n+1) |