Arithmetic sequence calculator
Find the nth term and partial sum of an arithmetic sequence.
What this calculator covers
Use this arithmetic sequence calculator to jump directly to any term and compute the partial sum from the start of the sequence.
It keeps the fixed step size visible so you can audit the nth-term formula and the arithmetic-series sum formula side by side.
Frequently asked questions
- What is an arithmetic sequence?
- An arithmetic sequence is a list of numbers where each term is produced by adding the same fixed value — the common difference — to the previous term. The sequence 2, 5, 8, 11 has a common difference of 3.
- How is the nth term calculated without listing every term?
- The formula a_n = a1 + (n − 1)d lets you jump directly to any position. You multiply the common difference by one less than the term index, then add the first term.
- What does the partial sum represent?
- The partial sum S_n is the total of all terms from the first term through the nth term. It is calculated with the formula n times the average of the first and nth term, which avoids adding each term individually.
- Can the common difference be negative or a decimal?
- Yes. A negative common difference produces a decreasing sequence, and decimal differences are fully supported. The calculator accepts any finite value for both the first term and the common difference.
Tool
Run the calculation
Result
RESULT · SEQUENCE
â„–213
Primary result
a8 = 26; S8 = 124
Starting from 5 and adding 3 each step gives a8 = 26 and S8 = 124.
- Preview terms
- 5, 8, 11, 14, 17
- Nth term
- 26
- Partial sum
- 124
- Term index
- 8
Step-by-step solution
- 1.Use a_n = a1 + (n - 1)d = 5 + (8 - 1)(3) to get 26.
- 2.Plug the first and nth terms into S_n = n(a1 + a_n) / 2.
- 3.Read the partial sum S8 as 124.
Walkthrough
Visual walkthrough
Arithmetic sequences move by a constant difference, so one formula finds any term and a second one totals the run from the start.
01
Fix the step size
d = 3
Every new term is the previous one plus the same constant difference.
02
Jump straight to the nth term
a8 = 26
The nth-term formula skips the manual listing process and lands on the requested position directly.
03
Add the run from term 1 to n
Using the first and nth terms together makes the arithmetic-series sum formula efficient.
S8 = 124