Sequence Sum Calculator
Sum arithmetic sequences.
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Result
What is a Sequence Sum Calculator?
A Sequence Sum Calculator computes the total of a number sequence, such as an arithmetic or geometric progression. It helps you quickly find the sum without manually adding each term.
How to calculate sequence sum manually (the formula)
For an arithmetic sequence with first term a, last term l, and n terms: S = n/2 × (a + l). For a geometric sequence with first term a and ratio r ≠ 1: S = a(rn − 1)/(r − 1).
Example calculation
Find the sum of the first 10 natural numbers (1, 2, 3, …, 10). Using S = n(n+1)/2: S = 10(11)/2 = 55.
Common mistakes
- Using the wrong formula — Arithmetic and geometric sequences have different sum formulas. Do not mix them up.
- Counting terms incorrectly — Make sure n is the correct number of terms, not the last value.
- Ignoring the sign of the ratio — For geometric sequences with a negative ratio, the sum formula still works but the sign alternates.
Frequently asked questions
What is a sequence sum?
A sequence sum is the total when you add up all terms in a sequence.
How do I find the sum of an arithmetic sequence?
Use the formula S = n/2 × (first + last), where n is the number of terms.
What is the difference between arithmetic and geometric sequences?
Arithmetic sequences have a constant difference; geometric sequences have a constant ratio.
How do I find the sum of the first n natural numbers?
Use S = n(n+1)/2.
What is a finite vs infinite sequence?
A finite sequence has a set number of terms; an infinite sequence continues forever.