Arithmetic Sequence Calculator
Calculate nth term and sum of arithmetic sequences
How to Use This Calculator
Select What to Find
Choose whether you want to find the nth term or the sum of the first n terms.
Enter the Values
Input the first term (a₁), common difference (d), and term number (n). All values must be valid numbers, and n must be a positive integer.
Click Calculate
Press the "Calculate" button to see the result displayed below.
Formula
nth Term: a_n = a₁ + (n - 1)d
Sum: S_n = n/2 × [2a₁ + (n-1)d]
Where:
- a_n = nth term
- a₁ = first term
- d = common difference
- n = term number
- S_n = sum of first n terms
Example: Find the 10th term of 2, 5, 8, 11, ...
a₁ = 2, d = 3, n = 10
a₁₀ = 2 + (10 - 1) × 3 = 2 + 27 = 29
About Arithmetic Sequence Calculator
An arithmetic sequence (also called arithmetic progression) is a sequence of numbers where each term after the first is obtained by adding a constant value called the common difference to the previous term. The arithmetic sequence calculator helps you find any term in the sequence and calculate the sum of the first n terms.
Key Features
- Find nth Term: Calculate any term in an arithmetic sequence
- Calculate Sum: Find the sum of the first n terms
- Simple Input: Just enter first term, common difference, and term number
- Instant Results: Get accurate calculations immediately
Common Applications
- Mathematical sequences and series problems
- Financial calculations (regular payments, savings)
- Time-based calculations (daily, weekly patterns)
- Pattern recognition and number sequences
Frequently Asked Questions
What is an arithmetic sequence?
An arithmetic sequence is a sequence where each term is obtained by adding a constant value (common difference) to the previous term. Example: 2, 5, 8, 11, 14, ... where the common difference is 3.
Can the common difference be negative?
Yes! A negative common difference creates a decreasing sequence. Example: 10, 7, 4, 1, -2, ... where d = -3.
What if n is not an integer?
The term number n must be a positive integer. The calculator will alert you if you enter a non-integer value.
How do I find the sum of terms?
Select "Sum of First n Terms" from the dropdown, enter your values, and click Calculate. The formula S_n = n/2 × [2a₁ + (n-1)d] will be used.
Can I use decimal numbers?
Yes, the first term and common difference can be any real numbers (including decimals and fractions). Only n must be an integer.