Arithmetic Sequence Calculator
Arithmetic Sequence Calculator
An arithmetic sequence adds the same fixed amount — the common difference — to get from one term to the next, and finding a term far down the sequence doesn't require listing every term that comes before it. Enter the first term, the common difference, and which term number you want, and this calculator jumps straight to that term using a direct formula, along with the running sum up to that point. It's a faster, more reliable approach than counting up manually, especially for sequences with many terms.
- In an arithmetic sequence, each term is found by adding a constant common difference to the previous term, e.g. 3, 8, 13, 18, 23… has a common difference of 5.
- The nth term formula skips ahead directly: aₙ = a₁ + (n−1)d, avoiding the need to list every term one by one.
- The sum of the first n terms uses the formula Sₙ = n/2 × (2a₁ + (n−1)d), which works by pairing the first and last terms and averaging.
How do I find the nth term of an arithmetic sequence?
Use the formula aₙ = a₁ + (n−1)d, where a₁ is the first term, d is the common difference, and n is the term number you want.
What is the 10th term of the sequence starting at 3 with a common difference of 5?
a₁₀ = 3 + (10−1)(5) = 3 + 45 = 48.
Arithmetic Sequence Calculator
An arithmetic sequence adds the same fixed amount — the common difference — to get from one term to the next, and finding a term far down the sequence doesn't require listing every term that comes before it. Enter the first term, the common difference, and which term number you want, and this calculator jumps straight to that term using a direct formula, along with the running sum up to that point. It's a faster, more reliable approach than counting up manually, especially for sequences with many terms.
- In an arithmetic sequence, each term is found by adding a constant common difference to the previous term, e.g. 3, 8, 13, 18, 23… has a common difference of 5.
- The nth term formula skips ahead directly: aₙ = a₁ + (n−1)d, avoiding the need to list every term one by one.
- The sum of the first n terms uses the formula Sₙ = n/2 × (2a₁ + (n−1)d), which works by pairing the first and last terms and averaging.
How do I find the nth term of an arithmetic sequence?
Use the formula aₙ = a₁ + (n−1)d, where a₁ is the first term, d is the common difference, and n is the term number you want.
What is the 10th term of the sequence starting at 3 with a common difference of 5?
a₁₀ = 3 + (10−1)(5) = 3 + 45 = 48.