Example 1
- a₁ = 1
- r = 2
- n = 5
9
What is the 5th term with a₁ = 1 and r = 2? 9. 1+(5−1)×2.
Arithmetic sequence term
Type the first term a₁, the common difference r and the index n. aₙ = a₁+(n−1)r. 1, 2 and 5 give 9. 3, 5 and 4 give 18. 10, −3 and 6 give −5.
n goes through max(1, the integer part of (n)). Typed 1.9 becomes 1. The result is raw, without trimming decimals. 2, 0.5 and 4 would show 3.5.
Results
Enter data and click Calculate.
How it works
The nth arithmetic term is the first term plus the step times (n−1). The calculator computes a₁+(n−1)r. 1, 2 and n = 5 give 1+8 = 9. The result goes into the field as a raw number, not a trimmed decimal string.
The fields are a₁, r and n. The IDs stay a, b, c. 3, 5 and 4 give 18. 10, −3 and 6 give −5, because a negative difference walks down. n is cut with floor and never drops below 1.
Typed n = 0 or n = 0.4 becomes 1, so you get a₁ back. n = 4.9 becomes 4. That is the its own card, not rounding of the result.
The nth geometric term multiplies by qⁿ⁻¹. The arithmetic series sum is on the neighbouring page and adds terms, it does not return one aₙ.
The header units switch does not multiply anything. 1, 2, 5 stay 9 whatever the label says.
1, 2 and 5 give 9. 3, 5 and 4 give 18. 10, −3 and 6 give −5.
Formula
aₙ = a₁ + (n−1)r, n = max(1, floor(n))
How to use
- Type a₁, r and n, for example 1, 2 and 5.
- Click Calculate. The nth term is 9.
- 3, 5 and 4 give 18. 10, −3 and 6 give −5.
- n = max(1, the integer part of (n)). Typed 1.9 counts as n = 1.
- The sum of that sequence lives on the arithmetic series card.
1, 2 and n = 5 give 9
aₙ = a₁+(n−1)r. n = max(1, the integer part of (n)). 1, 2 and 5 give 9. 3, 5 and 4 give 18. 10, −3 and 6 give −5.
- arithmetic
- A constant difference r. 1 and 2 at n = 5 give 9. 3 and 5 at n = 4 give 18.
- difference
- Field r. −3 with a₁ = 10 and n = 6 gives −5. A positive r walks up.
- term
- Index n after floor, never below 1. n = 1 returns a₁.
Examples
Example 2
- a₁ = 3
- r = 5
- n = 4
18
What is the 4th term with a₁ = 3 and r = 5? 18.
Example 3
- a₁ = 10
- r = −3
- n = 6
-5
What is the 6th term with a₁ = 10 and r = −3? -5. A raw JS minus.
Related calculators
Common questions
What is the 5th term with 1 and r = 2?
9. 1+(5−1)×2 = 9.
What does an arithmetic nth term mean?
Term number n in a sequence with a constant difference r. aₙ = a₁+(n−1)r.
What about 3, 5 and n = 4?
18. 3+3×5 = 18.
What about 10, −3 and n = 6?
−5. The result is -5, the raw number.
What does floor do to n?
n = max(1, the integer part of (n)). 4.9 becomes 4. 0 becomes 1 and returns a₁.
Does the result use six decimal places?
No. The calculator inserts the raw number. 3.5 would stay 3.5.
How is this different from a geometric term?
The calculator adds r. There you multiply by qⁿ⁻¹.
Where is the series sum?
On the arithmetic series sum card. Here one aₙ.
Does n = 1 return a₁?
Yes. (1−1)r = 0, a₁ remains.
Does a comma in 2.5 work?
Yes. a₁ = 2, r = 0.5, n = 4 give 3.5.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.