Sum of Series Calculator
Calculate sum of arithmetic and geometric series
How to Use This Calculator
Select Series Type
Choose between arithmetic series or geometric series.
Enter Values
Input the first term, common difference/ratio, and number of terms to sum.
Calculate Sum
Click "Calculate Sum" to see the sum of the series displayed.
Formulas
Arithmetic: S_n = n/2 × [2a₁ + (n-1)d]
where d is the common difference
Geometric: S_n = a₁ × (1 - rⁿ) / (1 - r), for r ≠ 1
If r = 1, then S_n = a₁ × n
Example 1: Sum of arithmetic series 2 + 5 + 8 + 11 + 14
a₁ = 2, d = 3, n = 5
S₅ = 5/2 × [2×2 + (5-1)×3] = 5/2 × [4 + 12] = 5/2 × 16 = 40
Example 2: Sum of geometric series 2 + 6 + 18 + 54
a₁ = 2, r = 3, n = 4
S₄ = 2 × (1 - 3⁴) / (1 - 3) = 2 × (1 - 81) / (-2) = 2 × (-80) / (-2) = 80
About Sum of Series Calculator
The sum of series calculator helps you find the sum of arithmetic and geometric series. A series is the sum of terms in a sequence, and this calculator provides quick calculations for both common types.
Arithmetic Series
- Sum of terms in an arithmetic sequence
- Example: 2 + 5 + 8 + 11 + 14 = 40
- Used in calculations involving linear patterns
Geometric Series
- Sum of terms in a geometric sequence
- Example: 2 + 6 + 18 + 54 = 80
- Used in exponential growth calculations, financial modeling
Frequently Asked Questions
What's the difference between a sequence and a series?
A sequence is a list of numbers (2, 5, 8, 11), while a series is the sum of those numbers (2 + 5 + 8 + 11 = 26).
Can I find the infinite sum of a geometric series?
For infinite geometric series, if |r| < 1, the sum converges to S_∞ = a₁ / (1 - r). This calculator focuses on finite sums.
What if the common ratio equals 1?
If r = 1 in a geometric series, all terms are equal, and the sum is simply S_n = a₁ × n.
Can I use negative values?
Yes! Both arithmetic and geometric series work with negative first terms and negative common differences/ratios.
How accurate are the results?
The calculator provides high precision results. Results are displayed with up to 6 decimal places for clarity.