# Arithmetic Sequence Calculator

URL: https://speedycalculator.com/calculators/math/arithmetic-sequence/
Last updated: 2026-10-25

> The arithmetic sequence calculator finds the nth term and the sum of the first n terms of a sequence that changes by a constant difference.

## Inputs

- First term (a₁)
- Common difference (d)
- Term number (n)

## Results

- nth term
- Sum of first n terms

## Formula

```
aₙ = a₁ + (n − 1)d
Sₙ = n(a₁ + aₙ) ÷ 2
```

## Explanation

Arithmetic sequences grow by adding the same amount each step, like 3, 7, 11, 15, …

### How to use the Arithmetic Sequence Calculator

- **First term (a₁)**
- **Common difference (d)**
- **Term number (n)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Multiply the common difference by n − 1 and add the first term. The sum averages the first and last terms and multiplies by n.

### Inputs explained

FieldWhat to enterFirst term (a₁)A numberCommon difference (d)A numberTerm number (n)A number

### What each result means

- **nth term** = [First term (a₁)] + ([Term number (n)] - 1)×[Common difference (d)]
- **Sum of first n terms** = [Term number (n)]×([First term (a₁)] + [nth term])÷2

### Example values

How the main result changes when **First term** changes and everything else stays at the example values above:

First term (a₁)nth term1.577.52.2578.253793.7579.754.580.5682

## Worked example

Inputs — First term (a₁): 3; Common difference (d): 4; Term number (n): 20.

Results — **nth term = 79**; Sum of first n terms = 820.

## Key terms

- **Common difference**: The fixed amount added to get the next term.

## FAQ

**How did Gauss add 1 to 100?**
Pairing terms: 50 pairs each summing to 101 gives 5,050.

**Can d be negative?**
Yes, the sequence then decreases.

**What formula does the Arithmetic Sequence Calculator use?**
aₙ = a₁ + (n − 1)d.